Elementary School Math Quiz: Graph And Interpret Coordinate Points
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Graph And Interpret Coordinate PointsQuestion 1 of 20

Four points are graphed on the coordinate plane.

What is the ordered pair for point K?

Question graphic
(3, 4)
(3, 5)
(5, 3)
(5, 4)
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Elementary School Math Quiz

Elementary School Math Quiz: Graph And Interpret Coordinate Points

Practice Graph And Interpret Coordinate Points in Elementary School Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Graph And Interpret Coordinate Points, giving you a quick way to practice the rules, question types, and explanations that matter most for Elementary School Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

Four points are graphed on the coordinate plane.

What is the ordered pair for point K?

  1. (3, 4)
  2. (3, 5)
  3. (5, 3) (correct answer)
  4. (5, 4)
Explanation: To locate point K, start at the origin and read across the x-axis first, then up the y-axis. Point K is 5 units to the right and 3 units up, so its ordered pair is (5, 3). Choice A gives the coordinates of point M. Choice B reverses the order of the two coordinates. Choice D reads the y-coordinate one gridline too high.

Question 2

Dara weighed her puppy at the end of each month. The graph shows her results.

What does the point labeled Q represent?

  1. At the end of month 3, the puppy weighed 6 pounds. (correct answer)
  2. At the end of month 6, the puppy weighed 3 pounds.
  3. During month 3, the puppy gained 6 pounds.
  4. During month 6, the puppy gained 3 pounds.
Explanation: In an ordered pair, the x-coordinate comes first. Point Q is at (3, 6), and the x-axis shows time in months while the y-axis shows weight in pounds, so the puppy weighed 6 pounds at the end of month 3. Choices B and D reverse the two coordinates. Choices C and D describe a gain during a month, but the height of a point gives the puppy's total weight, not the amount it gained.

Question 3

The graph shows the total distance Ravi had walked during his hike.

According to the graph, how many miles had Ravi walked after 4 hours?

  1. 2
  2. 4
  3. 6
  4. 8 (correct answer)
Explanation: Find 4 on the horizontal axis, move up to the line, then read across to the vertical axis. The line is at 8, so Ravi had walked 8 miles. Choice A is the number of miles he walked each hour. Choice B repeats the number of hours instead of reading the distance. Choice C reads the line at 3 hours instead of 4.

Question 4

Points R, S, and T are three vertices of a rectangle.

What ordered pair locates the fourth vertex of the rectangle?

  1. (2, 7)
  2. (7, 2) (correct answer)
  3. (7, 6)
  4. (7, 7)
Explanation: The fourth vertex must line up directly below point T and directly to the right of point R. That places it 7 units right and 2 units up, at (7, 2). Choice A reverses the coordinates. Choice C is point T, which is already a vertex. Choice D would not line up with point R, so the figure would not be a rectangle.

Question 5

A steady rain fell for 6 hours. The graph shows the amount of water in a rain barrel during that time.

How many gallons of water were in the barrel before the rain began?

  1. 0
  2. 1
  3. 3 (correct answer)
  4. 9
Explanation: Before the rain began, no time had passed, so look at the point where the line meets the vertical axis. That point is at a height of 3, so the barrel already held 3 gallons. Choice A assumes the barrel started empty, but the line does not begin at the origin. Choice B is the number of gallons added each hour. Choice D is the amount in the barrel after all 6 hours.

Question 6

The graph shows the locations of animals in a zoo on a coordinate grid. Each unit represents 10 meters. A zookeeper at the Lions' location needs to visit the Bears, then the Elephants, then return to the Lions. If the zookeeper can only walk along the grid lines (no diagonal walking), what is the total distance the zookeeper will walk?

  1. 180 meters because the total grid distance is 18 units
  2. 200 meters because the total grid distance is 20 units (correct answer)
  3. 220 meters because the total grid distance is 22 units
  4. 160 meters because the total grid distance is 16 units
Explanation: Lions are at (1, 3), Bears at (5, 6), Elephants at (8, 2). Distance from Lions to Bears: |5-1| + |6-3| = 4 + 3 = 7 units. Distance from Bears to Elephants: |8-5| + |2-6| = 3 + 4 = 7 units. Distance from Elephants back to Lions: |1-8| + |3-2| = 7 + 1 = 6 units. Total: 7 + 7 + 6 = 20 units. Since each unit is 10 meters: 20 × 10 = 200 meters.

Question 7

A delivery drone flies along straight horizontal and vertical paths, visiting points in this order: (0,0)(0,0), (0,6)(0,6), (9,6)(9,6), (9,0)(9,0), and back to (0,0)(0,0). Each grid unit represents 1 kilometer. What is the total distance the drone travels?

  1. 24 kilometers
  2. 15 kilometers
  3. 54 kilometers
  4. 30 kilometers (correct answer)
Explanation: Whenever a path traces out a shape on a grid, look at whether the points form a familiar figure—here they form a rectangle. When you plot (0,0)(0,0), (0,6)(0,6), (9,6)(9,6), and (9,0)(9,0), you get a rectangle that is 9 units wide and 6 units tall. Since the drone travels all the way around and back to start, the total distance is the perimeter. To find the perimeter, add up all four sides. The drone goes up 6 km, across 9 km, down 6 km, and back across 9 km:
6+9+6+9=30 kilometers.6 + 9 + 6 + 9 = 30 \text{ kilometers}.
You can also use the perimeter formula P=2(l+w)=2(9+6)=2(15)=30P = 2(l + w) = 2(9 + 6) = 2(15) = 30 km. That's why 30 kilometers is correct. The choice 15 kilometers only adds one length and one width (9+69 + 6)—that's half the trip, forgetting the drone travels each direction twice. The choice 24 kilometers comes from mistakenly using dimensions like 2(6+6)2(6+6) or miscounting the sides; it doesn't match the actual measurements. The choice 54 kilometers is the area (9×6=549 \times 6 = 54), which measures the space inside the rectangle, not the distance around it—a very common mix-up. The key trap here is confusing perimeter (distance around) with area (space inside). When a question asks about total distance traveled along the edges, you always want perimeter. Remember: perimeter is addition of side lengths, while area is multiplication.

Question 8

On a treasure map, each grid unit represents 5 meters, and the origin is the starting flag. A treasure chest is located at the point (4,6)(4, 6). How far east of the flag, in actual meters, is the treasure chest?

  1. 24 meters
  2. 4 meters
  3. 30 meters
  4. 20 meters (correct answer)
Explanation: Whenever you work with a coordinate grid that has a scale, remember that each point tells you a direction and distance in units, and the scale converts those units into real-world measurements. The key is knowing which number in the point (x,y)(x, y) points which way: the first number is horizontal (east-west), and the second is vertical (north-south). The treasure chest sits at (4,6)(4, 6). Since "east" is the horizontal direction, you focus on the first number, 44. That means the chest is 44 grid units east of the flag. Each unit equals 55 meters, so you multiply: 4×5=204 \times 5 = 20 meters. That's why 20 meters is correct. Now look at the traps. The choice 24 meters comes from adding 4+6=104 + 6 = 10 or mixing up numbers, but "east" only uses the horizontal value, not both. The choice 4 meters ignores the scale entirely — it gives the number of units instead of converting to meters. The choice 30 meters uses the wrong coordinate: it multiplies 6×56 \times 5, which would tell you how far north the chest is, not east. Only 20 meters uses the correct coordinate and applies the scale. A helpful tip: on scale-map questions, always ask two questions in order — "Which coordinate matches the direction asked?" and "Have I multiplied by the scale?" Missing either step is the most common way to land on a wrong answer. Remember: xx = east/west, yy = north/south.

Question 9

A hiker's distance from the trailhead is recorded every hour and plotted as points in the form (hours, miles from trailhead). Two of the recorded points are (2,6)(2, 6) and (5,6)(5, 6). Based on these two points, what most likely happened between hour 2 and hour 5?

  1. The hiker turned around and walked all the way back to the trailhead before hour 5.
  2. The hiker walked an additional 6 miles farther from the trailhead during those hours.
  3. The hiker rested and did not move farther from the trailhead, since the distance stayed at 6 miles. (correct answer)
  4. The hiker's speed increased because more time passed at the same location.
Explanation: Whenever you read points on a graph, remember what each number stands for. Here, the pairs are written as (hours, miles from trailhead). The first number tells you when, and the second number tells you how far the hiker is from the start. Look closely at the two points: (2,6)(2, 6) and (5,6)(5, 6). The time changed from hour 22 to hour 55, but the distance stayed exactly the same — 66 miles both times. If the distance from the trailhead didn't change, then the hiker didn't get any farther away. The most reasonable explanation is that the hiker rested and stayed at the 66-mile mark. The idea that the hiker "turned around and walked all the way back to the trailhead" would require the distance to drop to 00, but it's still 66, so that's wrong. The claim that the hiker "walked an additional 6 miles farther" misreads the 66 as a change in distance — but 66 is the position, not an amount added, and the position never changed. The statement that "the hiker's speed increased" doesn't fit either: standing still means zero movement, so speed didn't go up at all. The trap here is confusing a value that stays the same with change. When the second coordinate is identical in two points, nothing moved during that stretch. Always compare each coordinate separately — ask "did the time change?" and "did the distance change?" — before deciding what happened.

Question 10

A vendor's stand is plotted at the point (6,0)(6, 0) on a coordinate grid representing a fairground, where the origin is the main gate. Which statement is true about the vendor's stand?

  1. The stand lies on the y-axis, 6 units above the gate, since the first number tells how far up to move.
  2. The stand lies on the x-axis, 6 units to the right of the gate, since the first number tells how far right to move. (correct answer)
  3. The stand sits diagonally, 6 units right and 6 units up from the gate, since the pair describes a slanted path.
  4. The stand lies on the y-axis, 6 units to the right of the gate, since the second number sets the horizontal move.
Explanation: An ordered pair like (6,0)(6, 0) always reads in a fixed order: the first number is left-right (the x-coordinate), and the second is up-down (the y-coordinate). Starting from the gate at (0,0)(0, 0), you go 6 units right, then 0 units up. Because the second number is 0, you never leave the x-axis, so the stand sits on the x-axis, 6 units to the right of the gate. The choice placing the stand on the y-axis, 6 units up treats the 6 as an up-and-down move, but 6 is the first number, so it is a left-right move. The choice putting it 6 units right and 6 units up invents a second 6; the pair only has one 6 and a 0, so there is no upward move. The choice that says the stand lies on the y-axis but 6 units to the right mixes things up too—if you move right, you are along the x-axis, not the y-axis, and it wrongly ties the horizontal move to the second number. Study tip: always read ordered pairs as (right/left, up/down) in that exact order. A zero just means "stay put" along that axis.

Question 11

Two students are asked to plot a point that is 3 units to the right of the origin and 8 units above it. Student A plots the point at (3,8)(3, 8). Student B plots the point at (8,3)(8, 3). Which student plotted the point correctly?

  1. Student B, because the first number in an ordered pair tells how far up a point is.
  2. Student A, because the x-coordinate (horizontal distance) is written first, then the y-coordinate (vertical distance). (correct answer)
  3. Both students, because the order of the two coordinates does not change a point's location.
  4. Neither student, because the point should be written as (8,8)(8, 8) to combine both movements.
Explanation: Whenever you plot a point on the coordinate plane, remember that an ordered pair follows a strict rule: the numbers always come in the order (x,y)(x, y). The first number is the x-coordinate, telling you how far to move horizontally (right or left), and the second number is the y-coordinate, telling you how far to move vertically (up or down). A helpful way to remember: you walk across the floor before you climb the stairs — right first, then up. Here, the point is 3 units to the right (a horizontal move) and 8 units up (a vertical move). So the x-coordinate is 33 and the y-coordinate is 88, giving (3,8)(3, 8). That means the student who plotted it as (3,8)(3, 8) because the horizontal distance is written first, then the vertical distance is correct. The choice claiming the point should be (8,3)(8, 3) because the first number tells how far up reverses the rule — it wrongly puts the vertical distance first. Saying both students are right because order doesn't matter is a common trap; order absolutely matters, since (3,8)(3, 8) and (8,3)(8, 3) are two completely different locations. And the choice claiming the answer is (8,8)(8, 8) to combine both movements invents a rule that doesn't exist — you never add or merge the two distances; each stays in its own position. On these questions, always double-check which number is horizontal and which is vertical. Repeat the phrase "right, then up" or "x before y" to lock in the correct order.

Question 12

A point is described as being located 5 units to the right of the y-axis and exactly on the x-axis. Which ordered pair represents this point?

  1. (5,5)(5, 5)
  2. (0,5)(0, 5)
  3. (5,0)(5, 0) (correct answer)
  4. (2,5)(2, 5)
Explanation: An ordered pair is written as (x, y): the first number tells how far to move left or right, and the second tells how far to move up or down. "5 units to the right of the y-axis" means the x-coordinate is 5. "Exactly on the x-axis" means the point has not moved up or down, so the y-coordinate is 0. Together that gives (5, 0). The pair (5, 5) moves 5 right and 5 up, but nothing said to move up, so it ignores "on the x-axis." The pair (0, 5) moves 0 right and 5 up, placing the point on the y-axis instead of 5 units to the right of it. The pair (2, 5) moves only 2 right and 5 up, so both numbers are wrong. Remember: a point on the x-axis always has a y-coordinate of 0, and a point on the y-axis always has an x-coordinate of 0. Knowing which axis forces which zero helps you every time.

Question 13

A rectangular garden is plotted on a coordinate grid with corners at (2,2)(2, 2), (2,9)(2, 9), (10,9)(10, 9), and (10,2)(10, 2), where each grid unit equals 1 meter. What is the area of the garden, in square meters?

  1. 15 square meters
  2. 56 square meters (correct answer)
  3. 63 square meters
  4. 72 square meters
Explanation: Whenever you see a shape plotted on a coordinate grid, the trick is to use the coordinates to find the side lengths. For a rectangle, you find the length of each side by counting the distance between corners along the grid, then use the formula Area = length × width. Start by finding the two dimensions. Look at the corners that share the same xx-value, like (2,2)(2, 2) and (2,9)(2, 9). Since the xx stays the same, this is a vertical side, and its length is the difference in the yy-values: 9−2=79 - 2 = 7 meters. Now look at (2,2)(2, 2) and (10,2)(10, 2), which share the same yy-value. This horizontal side has length 10−2=810 - 2 = 8 meters. Multiply the two sides: 8×7=568 \times 7 = 56 square meters. The choice 63 square meters comes from mistakenly using 9×7=639 \times 7 = 63 — that treats one coordinate as a length instead of subtracting to find the true distance. The choice 72 square meters comes from 8×98 \times 9, again forgetting to subtract to get the correct side length of 77. The choice 15 square meters comes from adding the two sides (8+7=158 + 7 = 15) instead of multiplying — that's the perimeter-style mistake, not area. A reliable strategy: to find a side length on a grid, always subtract the coordinates that change, never just read a single number off a corner. Then remember area means multiply, while perimeter means add.

Question 14

On a city map, three landmarks are plotted: the library at (4,9)(4, 9), the school at (4,2)(4, 2), and the park at (11,2)(11, 2). Which two landmarks lie directly north-south of each other along the same vertical line?

  1. The library and the park
  2. The school and the park
  3. The library and the school (correct answer)
  4. All three landmarks lie on the same vertical line
Explanation: Whenever you plot points as ordered pairs (x,y)(x, y), remember that the first number tells you how far right (east) you go, and the second number tells you how far up (north) you go. Two points lie on the same vertical (north-south) line when they share the same x-coordinate — they're directly above or below each other. Two points lie on the same horizontal (east-west) line when they share the same y-coordinate. Look at the x-coordinates: the library is at (4,9)(4, 9) and the school is at (4,2)(4, 2). Both have an x-coordinate of 44, so they stack up along the same vertical line — one is directly north of the other. That's why the library and the school is correct. The pairing of the library and the park fails because their x-coordinates are 44 and 1111 — different columns, so no shared vertical line. The pairing of the school and the park also has x-coordinates 44 and 1111; these actually share the same y-coordinate of 22, meaning they lie east-west of each other, not north-south. The claim that all three landmarks lie on the same vertical line can't be true, since the park at x=11x = 11 sits far to the right of the other two. A helpful trap-avoider: "same x = up-and-down, same y = side-to-side." When a question asks about north-south, hunt for matching x-coordinates; when it asks east-west, hunt for matching y-coordinates.

Question 15

In a park map, distances are measured in meters using a coordinate grid, with the gate at the origin (0,0)(0,0). The x-axis measures how far east of the gate a location is, and the y-axis measures how far north of the gate a location is. A bench is plotted at the point (7,3)(7, 3). Which statement correctly describes the bench's location?

  1. The bench is 7 meters east and 3 meters north of the gate. (correct answer)
  2. The bench is 3 meters east and 7 meters north of the gate.
  3. The bench is 10 meters east and 10 meters north of the gate.
  4. The bench is 4 meters east and 3 meters north of the gate.
Explanation: An ordered pair like (7,3)(7, 3) is read left to right: the first number is the x-coordinate and the second is the y-coordinate. On this map, x measures meters east and y measures meters north. So the 7 means 7 meters east, and the 3 means 3 meters north — that makes "7 meters east and 3 meters north" correct. The choice saying "3 meters east and 7 meters north" swaps the two numbers, which happens when you forget that the x-coordinate comes first. The choice saying "10 meters east and 10 meters north" adds the numbers together (7+3=107 + 3 = 10), but coordinates are two separate directions and should never be combined. The choice saying "4 meters east and 3 meters north" keeps the north distance right but subtracts to get the east distance (7−3=47 - 3 = 4); the east distance is just the first number, 7, not a difference. Your takeaway: read every ordered pair as (across, up), and match each number to its own axis before choosing.

Question 16

A rectangular garden plot is drawn on a coordinate grid. Three of its corners are located at (2,3)(2, 3), (2,9)(2, 9), and (8,3)(8, 3). What are the coordinates of the fourth corner needed to complete the rectangle?

  1. (8,9)(8, 9) (correct answer)
  2. (6,6)(6, 6)
  3. (9,8)(9, 8)
  4. (8,6)(8, 6)
Explanation: A rectangle has matching pairs of sides, so each coordinate value should appear exactly twice among the four corners. The given corners have x-values 2, 2, and 8, so the missing corner needs x = 8 to pair with the lonely 8. The given y-values are 3, 9, and 3, so the missing corner needs y = 9 to pair with the lonely 9. That gives (8,9)(8, 9), sitting directly across from (2,3)(2, 3) to square off the rectangle. The point (6,6)(6, 6) is wrong because it comes from averaging or guessing a middle spot; it doesn't line up with any existing corner's x or y, so it can't form a right angle here. The point (9,8)(9, 8) is tempting because it uses an 8 and a 9, but the numbers are swapped. Coordinates are written as (x,y)(x, y), so this lands at a different spot off the rectangle. The point (8,6)(8, 6) correctly uses x = 8, but its y-value of 6 matches none of the given corners. A fourth corner must share its y with an existing corner, and 6 never appears, so it won't close the shape.

Question 17

Look at the coordinate plane shown. Point A represents a playground, and Point B represents a library. Sarah walks from the playground directly east for 200 meters, then directly north for 150 meters to reach the school at Point C. What are the coordinates of Point C?

  1. (3, 4) because she moved 3 units east and then 4 units north from the playground
  2. (5, 6) because she moved 3 units east and then 4 units north from the playground
  3. (6, 5) because she moved 4 units east and then 3 units north from the playground (correct answer)
  4. (4, 6) because she moved 4 units east and then 3 units north from the playground
Explanation: The playground, Point A, is at (2, 2), and each unit on the grid stands for 50 meters. Walking 200 meters east means 200 ÷ 50 = 4 units east, and 150 meters north means 150 ÷ 50 = 3 units north. Starting at (2, 2) and adding 4 units east and 3 units north gives (2 + 4, 2 + 3) = (6, 5). The choice (3, 4) swaps east and north amounts and also forgets to start from (2, 2). The choice (5, 6) uses the wrong movement, treating east as 3 and north as 4, so its coordinates land in the wrong spot. The choice (4, 6) uses the correct 4 east and 3 north but then adds them in the wrong order, writing north before east instead of (east, north). Remember: in a coordinate pair, the first number is how far right (east) and the second is how far up (north).

Question 18

Maya is tracking the temperature of her science experiment over several days. She records the data on a coordinate plane where the x-axis represents the day number and the y-axis represents the temperature in degrees Celsius. On day 3, the temperature was 25°C. On day 7, the temperature was 41°C. If the temperature increased at a steady rate, what was the temperature on day 5?

  1. 29°C, found by adding just 4°C to the day 3 temperature of 25°C
  2. 33°C, found by adding 8°C to the day 3 temperature of 25°C (correct answer)
  3. 31°C, found by averaging the day 3 and day 7 temperatures of 25°C and 41°C
  4. 35°C, found by adding 5°C for each day from day 3 to day 5
Explanation: From day 3 to day 7 is 4 days, and the temperature rose from 25°C to 41°C, an increase of 16°C. That is a steady rate of 16 ÷ 4 = 4°C per day. Day 5 is 2 days after day 3, so the temperature went up 2 × 4 = 8°C, giving 25 + 8 = 33°C. The choice that adds only 4°C to get 29°C moves ahead just one day instead of two. The choice giving 31°C simply averages the day 3 and day 7 temperatures; the midpoint value happens to be for day 5, but 31°C is not the correct sum since the true midpoint temperature is 33°C. The choice giving 35°C uses a wrong rate of 5°C per day instead of the actual 4°C per day.

Question 19

Two mailboxes are plotted on a neighborhood coordinate grid, where each unit equals 1 meter. Mailbox A is at (3,5)(3, 5) and Mailbox B is at (11,5)(11, 5). What is the actual distance, in meters, between the two mailboxes measured along a straight horizontal path?

  1. 8 meters, the gap found by subtracting the smaller x-value from the larger x-value (correct answer)
  2. 14 meters, the total found by adding the two x-values of the mailboxes together
  3. 16 meters, the total found by adding all four coordinate numbers from both points
  4. 6 meters, the gap found by subtracting the two y-values from the larger x-value
Explanation: Both mailboxes share a y-coordinate of 5, so they sit on the same horizontal line. To find how far apart they are, you look only at the x-values and subtract the smaller from the larger: 11 - 3 = 8. Since each unit is 1 meter, the mailboxes are 8 meters apart. That matches the choice describing the gap between the x-values. The choice giving 14 meters adds the x-values (11 + 3) instead of subtracting them, but distance is the gap between points, not their sum. The choice giving 16 meters adds all four numbers (3 + 5 + 11 + 5), which mixes together x- and y-values that measure different directions. The choice giving 6 meters subtracts the two y-values from an x-value, combining coordinates in a way that does not measure horizontal distance at all. A reliable rule: when two points share a coordinate, subtract the coordinates that are different, taking the larger minus the smaller so your answer stays positive. Same y-values give a horizontal distance from the x-values; same x-values would give a vertical distance from the y-values.

Question 20

Starting at the point (2,4)(2, 4) on a coordinate grid, a student moves 5 units to the right and then 3 units up to plot a second point. What are the coordinates of the second point?

  1. (2,7)(2, 7)
  2. (5,3)(5, 3)
  3. (7,4)(7, 4)
  4. (7,7)(7, 7) (correct answer)
Explanation: Whenever you move points around a coordinate grid, remember what each number in an ordered pair (x,y)(x, y) controls: the first number is the x-coordinate (left/right position) and the second number is the y-coordinate (up/down position). Moving right increases the x-coordinate; moving up increases the y-coordinate. Start at (2,4)(2, 4). Moving 5 units to the right means adding 5 to the x-coordinate: 2+5=72 + 5 = 7. Moving 3 units up means adding 3 to the y-coordinate: 4+3=74 + 3 = 7. That lands you at (7,7)(7, 7). Now look at why the other choices trip students up. The point (2,7)(2, 7) correctly adds 3 to the y-coordinate but forgets to move right at all — it ignores the horizontal step. The point (5,3)(5, 3) comes from using the movement amounts (55 right and 33 up) as the coordinates, forgetting to start from (2,4)(2, 4). The point (7,4)(7, 4) correctly moves 5 right to get x=7x = 7, but leaves the y-coordinate unchanged — it forgets the "3 units up" step entirely. The trap here is doing only part of the motion or confusing the movement distances with the final position. A helpful strategy: handle the two coordinates separately. Ask "What happens to x?" then "What happens to y?" Add each change to the matching starting number. Keeping x and y in their own columns keeps you from mixing them up or skipping a step.