Reading Coordinates
Help Questions
ISEE Lower Level: Mathematics Achievement › Reading Coordinates
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?
(4, 2)
(10, 9)
(9, 10)
(2, 4)
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?
(5, 15)
(13, 9)
(5, 9)
(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).
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?
(10, 8)
(0, 8)
(5, 3)
(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).
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?
(6, 8)
(4, 5)
(7, 7)
(8, 6)
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?
(7, 9)
(9, 7)
(2, 3)
(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).
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?
(8, 3)
(8, 13)
(8, 5)
(3, 8)
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?
(7, 0)
(0, 0)
(0, 7)
(7, 7)
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?
(9, 6)
(6, 9)
(5, 9)
(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).
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?
(8, 2)
(1, 4)
(2, 8)
(3, 12)
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?
(4, 8)
(6, 4)
(4, 6)
(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).