ISEE Lower Level Mathematics Achievement Quiz: Reading Coordinates

What this quiz covers

This quiz focuses on Reading Coordinates, giving you a quick way to practice the rules, question types, and explanations that matter most for ISEE Lower Level Mathematics Achievement.

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.

Question 1

1. (9, 10)
2. (2, 4)
3. (4, 2) (correct answer)
4. (10, 9)

Explanation: The x-coordinate of Point C must be the same as the x-coordinate of Point B, which is 4. The y-coordinate of Point C must be the same as the y-coordinate of Point A, which is 2. Combining these, the coordinates of Point C are (4, 2).

Question 2

1. (0, 8) (correct answer)
2. (10, 8)
3. (5, 3)
4. (8, 0)

Explanation: The starting point is (5, 8). Moving 5 units to the left affects the x-coordinate. We subtract 5 from the starting x-coordinate: $5 - 5 = 0$. The y-coordinate does not change. The new point's coordinates are (0, 8).

Question 3

1. (5, 9)
2. (6, 9) (correct answer)
3. (9, 6)
4. (1, 5)

Explanation: The entrance and fountain are on a horizontal line because their y-coordinates are both 9. The bench's y-coordinate must also be 9. To find the x-coordinate of the bench, find the number exactly halfway between 1 and 11. The average is $(1 + 11) / 2 = 12 / 2 = 6$. So, the bench is at (6, 9).

Question 4

1. (4, 6) (correct answer)
2. (6, 4)
3. (4, 8)
4. (4, 4)

Explanation: The oak tree and the cave are on a vertical line because their x-coordinates are both 4. The well's x-coordinate must also be 4. To find the y-coordinate, find the number exactly halfway between 10 and 2. The average is $(10 + 2) / 2 = 12 / 2 = 6$. So, the well is at (4, 6).

Question 5

1. (4, 5)
2. (6, 5)
3. (8, 5) (correct answer)
4. (9, 5)

Explanation: The points are on a horizontal line, so the y-coordinate of B is 5. The distance between the x-coordinates of A and C is $10 - 2 = 8$. Let the distance from C to B be $d$. Then the distance from A to B is $3d$. The total distance is $d + 3d = 8$, so $4d = 8$, which means $d = 2$. Point B is 2 units away from C. Since B is between A and C, its x-coordinate is $10 - 2 = 8$. The coordinates of B are (8, 5).

Question 6

1. (5, 0) (correct answer)
2. (0, 5)
3. (0, 6)
4. (5, 6)

Explanation: The school is at (5, 6). A point on the same vertical line as the school must have the same x-coordinate, so its x-coordinate is 5. The library is at (0, 0). A point on the same horizontal line as the library must have the same y-coordinate, so its y-coordinate is 0. Therefore, the fire station is at (5, 0).

Question 7

1. (12, 1)
2. (8, 11)
3. (7, 12)
4. (12, 7) (correct answer)

Explanation: Since all points are on the same vertical line, their x-coordinates must be the same. The x-coordinate of Point H is 12. The y-coordinate of Point H is 4 less than the y-coordinate of Point G (11). So, the y-coordinate is $11 - 4 = 7$. The coordinates of Point H are (12, 7).

Question 8

1. (8, 5)
2. (5, 8)
3. (8, 9) (correct answer)
4. (3, 8)

Explanation: The distance between (3, 4) and (8, 4) is $8 - 3 = 5$ units. This is the side length of the square. Since the square is in the first quadrant, the other two corners must be 5 units directly above the given points. The point above (3, 4) is (3, 4+5) = (3, 9). The point above (8, 4) is (8, 4+5) = (8, 9). Of the choices given, (8, 9) is a possible corner.

Question 9

1. (5, 9)
2. (13, 9) (correct answer)
3. (5, 15)
4. (13, 15)

Explanation: The move was 4 units left and 3 units up. To reverse this move, you must go 4 units right and 3 units down from the landing spot (9, 12). Moving 4 units right means adding 4 to the x-coordinate: $9 + 4 = 13$. Moving 3 units down means subtracting 3 from the y-coordinate: $12 - 3 = 9$. The starting position was (13, 9).

Question 10

1. (4, 12)
2. (16, 0)
3. (8, 8) (correct answer)
4. (16, 16)

Explanation: Let the coordinates be (x, y). We are told that x = y and x + y = 16. Since x and y are the same, we can write the second equation as x + x = 16, or 2x = 16. Solving for x gives x = 8. Since y = x, y is also 8. The coordinates are (8, 8).

Question 11

1. (2, 3)
2. (7, 9)
3. (9, 7) (correct answer)
4. (9, 3)

Explanation: The vertices of a rectangle with sides parallel to the axes share x and y coordinates. The given points are (3, 2), (9, 2), and (3, 7). The x-coordinates in use are 3 and 9. The y-coordinates in use are 2 and 7. The fourth corner must use the remaining combination of one x-coordinate and one y-coordinate. Therefore, the fourth corner is at (9, 7).

Question 12

1. (8, 5)
2. (3, 8)
3. (8, 13)
4. (8, 3) (correct answer)

Explanation: The x-coordinate is given as 8. The y-coordinate is '5 less than the x-coordinate', which means we subtract 5 from the x-coordinate: $8 - 5 = 3$. So, the y-coordinate is 3. The coordinates of the point are (8, 3).

Question 13

1. (0, 7)
2. (7, 0) (correct answer)
3. (7, 7)
4. (0, 0)

Explanation: Any point on the x-axis has a y-coordinate of 0. Since Point M is 7 units to the right of the origin, its x-coordinate is 7. Therefore, the coordinates of point M are (7, 0).

Question 14

1. (6, 8) (correct answer)
2. (8, 6)
3. (4, 5)
4. (7, 7)

Explanation: To find the final coordinates, add the movements to the starting coordinates. The starting x-coordinate is 2. Moving 4 units right means adding 4, so the new x-coordinate is $2 + 4 = 6$. The starting y-coordinate is 3. Moving 5 units up means adding 5, so the new y-coordinate is $3 + 5 = 8$. The final location is at (6, 8).

Question 15

1. (1, 4)
2. (2, 8) (correct answer)
3. (3, 12)
4. (8, 2)

Explanation: The prime numbers are 2, 3, 5, 7, etc. The smallest prime number is 2. So, the x-coordinate is 2. The y-coordinate is 4 times the x-coordinate, which is $4 \times 2 = 8$. The coordinates of the point are (2, 8).

Question 16

1. (4, 4) (correct answer)
2. (16, 12)
3. (4, 8)
4. (10, 2)

Explanation: To find the new coordinates, adjust the starting point (10, 8). Moving 6 units to the left means subtracting 6 from the x-coordinate: $10 - 6 = 4$. Moving 4 units down means subtracting 4 from the y-coordinate: $8 - 4 = 4$. The squirrel's new coordinates are (4, 4).

Question 17

1. (7, 8)
2. (13, 8) (correct answer)
3. (8, 13)
4. (13, 22)

Explanation: Start with the coordinates (10, 15). Moving 3 units to the right means adding 3 to the x-coordinate: $10 + 3 = 13$. Moving 7 units down means subtracting 7 from the y-coordinate: $15 - 7 = 8$. The new coordinates are (13, 8).

Question 18

1. 16 units
2. 20 units (correct answer)
3. 24 units
4. 10 units

Explanation: First, identify the fourth vertex. The x-coordinates are 1 and 7, and the y-coordinates are 1 and 5. The fourth vertex must be at (7, 5). The side lengths can be found from the coordinates. The horizontal length is the difference in x-coordinates: $7 - 1 = 6$ units. The vertical length is the difference in y-coordinates: $5 - 1 = 4$ units. The perimeter of a rectangle is $2 \times (\text{length} + \text{width}) = 2 \times (6 + 4) = 2 \times 10 = 20$ units.

Question 19

1. (0, 5)
2. (11, 0)
3. (11, 5)
4. (5, 11) (correct answer)

Explanation: The horizontal distance from the y-axis defines the x-coordinate. So, the x-coordinate is 5. The vertical distance from the x-axis defines the y-coordinate. So, the y-coordinate is 11. The coordinates of Point Q are (5, 11).

Question 20

1. (5, 5) (correct answer)
2. (5, 11)
3. (3, 5)
4. (5, 3)

Explanation: The spider starts at (0, 8). Crawling 5 units to the right means adding 5 to the x-coordinate: $0 + 5 = 5$. Crawling 3 units down means subtracting 3 from the y-coordinate: $8 - 3 = 5$. The new position is (5, 5).