ISEE Lower Level Mathematics Achievement Quiz
Practice Reading Coordinates in ISEE Lower Level Mathematics Achievement with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.
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Point A is at (9, 2) and Point B is at (4, 10). The x-coordinate of Point C is the same as the x-coordinate of Point B. The y-coordinate of Point C is the same as the y-coordinate of Point A. What are the coordinates of Point C?
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.
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.
Point A is at (9, 2) and Point B is at (4, 10). The x-coordinate of Point C is the same as the x-coordinate of Point B. The y-coordinate of Point C is the same as the y-coordinate of Point A. What are the coordinates of Point C?
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).
A game piece lands on (9, 12). To find its starting position, you must reverse its last move, which was 4 units left and 3 units up. What were the coordinates of the game piece's starting position?
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).
The point (5, 8) is plotted on a grid. A new point is plotted 5 units directly to the left of (5, 8). What are the coordinates of this new point?
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).
A robot starts at the point (2, 3) on a coordinate grid. It is programmed to move 4 units to the right and then 5 units up. What are the coordinates of the robot's final location?
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).
Three corners of a rectangle are located at the points (3, 2), (9, 2), and (3, 7). What are the coordinates of the fourth corner of the rectangle?
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).
A point is located on a coordinate grid. Its x-coordinate is 8. Its y-coordinate is 5 less than its x-coordinate. What are the coordinates of the point?
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).
Point M is located on the x-axis. It is 7 units to the right of the origin (0, 0). What are the coordinates of point M?
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).
A park entrance is at (1, 9). A water fountain is at (11, 9). A bench is located exactly halfway between the entrance and the fountain. What are the coordinates of the bench?
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).
A point is located in the first quadrant. Its x-coordinate is the smallest prime number. Its y-coordinate is 4 times its x-coordinate. What are the coordinates of the point?
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).
A treasure map shows three locations: the oak tree at (4, 10), the cave at (4, 2), and the well. The well is located exactly halfway between the oak tree and the cave. What are the coordinates of the well?
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).
A squirrel is at the point (10, 8). It scurries 6 units to the left and then 4 units down. What are the squirrel's new coordinates?
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).
A kite is flying at the position represented by (10, 15). A gust of wind blows it 3 units to the right and 7 units down. What are the new coordinates of the kite?
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).
Points A, B, and C all lie on the same horizontal line. Point A is at (2, 5) and Point C is at (10, 5). Point B is located between A and C, and it is 3 times as far from A as it is from C. What are the coordinates of Point B?
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).
The points (3, 4) and (8, 4) are two adjacent corners of a square on a coordinate grid. If the entire square lies in the first quadrant, which of the following points is another corner of the square?
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.
Points (1, 1), (1, 5), and (7, 1) are three vertices of a rectangle. What is the perimeter of the rectangle?
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.
On a map, the library is at the origin (0, 0). The school is at (5, 6). The fire station is on the same vertical line as the school and on the same horizontal line as the library. What are the coordinates of the fire station?
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).
Point Q is located on a grid. Its horizontal distance from the y-axis is 5 units. Its vertical distance from the x-axis is 11 units. If Point Q is in the first quadrant, what are its coordinates?
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).
A spider starts building a web at (0, 8). It crawls 5 units to the right and then 3 units down. What are the coordinates of the spider's new position?
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).
The sum of the coordinates of Point P is 16. Its x-coordinate and y-coordinate are identical. What are the coordinates of Point P?
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).
Points F, G, and H are all on the same vertical line. Point F is at (12, 5) and Point G is at (12, 11). The y-coordinate of Point H is 4 less than the y-coordinate of Point G. What are the coordinates of Point H?
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).