Reading Coordinates - ISEE Lower Level Mathematics Achievement

1. What are the coordinates of the point that is $3$ units right of the origin and on the $x$-axis?

   $(3, 0)$. Points on the $x$-axis have $y=0$, and right of the origin means a positive $x$-coordinate.

2. What does the first number in an ordered pair $(x, y)$ represent on a grid?

   $x$-coordinate (horizontal position). The first number indicates the horizontal distance from the origin along the $x$-axis.

3. What are the coordinates of a point that is $1$ unit right and $8$ units down from the origin?

   $(1, -8)$. Moving right from the origin gives a positive $x$-coordinate, and down gives a negative $y$-coordinate.

4. Which ordered pair has the same location as "$2$ units left and $5$ units up"?

   $(-2, 5)$. Left movement corresponds to a negative $x$-value, and up corresponds to a positive $y$-value from the origin.

5. What is the coordinate of any point located on the $x$-axis (in terms of $y$)?

   $y = 0$. Any point on the $x$-axis has no vertical displacement from the origin, so its $y$-coordinate is zero.

6. Which direction does the $y$-coordinate increase on a standard coordinate grid?

   Upward. Positive $y$-values increase as you move upward from the origin along the $y$-axis.

7. Identify the point with $x = -3$ and $y = 6$ as an ordered pair.

   $(-3, 6)$. The ordered pair is formed by placing the given $x$-value first and $y$-value second.

8. Find the missing coordinate: If a point is $(8, y)$ on the $x$-axis, what is $y$?

   $0$. Points on the $x$-axis require the $y$-coordinate to be zero regardless of the $x$-value.

9. Identify the point with $x = 10$ and $y = -2$ as an ordered pair.

   $(10, -2)$. The ordered pair is formed by placing the given $x$-value first and $y$-value second.

10. What is the name of the point where the $x$-axis and $y$-axis intersect?

    The origin, $(0, 0)$. The axes intersect at the reference point called the origin, where both coordinates are zero.

11. What is the name of the vertical axis on a coordinate grid?

    $y$-axis. The vertical axis runs up and down and is labeled as the $y$-axis in a coordinate plane.

12. What are the coordinates of a point that is $4$ units right and $3$ units up from the origin?

    $(4, 3)$. Moving right from the origin gives a positive $x$-coordinate, and up gives a positive $y$-coordinate.

13. Find the missing coordinate: If a point is $(x, -5)$ on the $y$-axis, what is $x$?

    $0$. Points on the $y$-axis require the $x$-coordinate to be zero regardless of the $y$-value.

14. What does the second number in an ordered pair $(x, y)$ represent on a grid?

    $y$-coordinate (vertical position). The second number indicates the vertical distance from the origin along the $y$-axis.

15. Which ordered pair has the same location as "$7$ units right and $1$ unit down"?

    $(7, -1)$. Right movement corresponds to a positive $x$-value, and down corresponds to a negative $y$-value from the origin.

16. Identify the coordinates of a point on the $y$-axis that is $9$ units above the origin.

    $(0, 9)$. Points on the $y$-axis have $x=0$, and above the origin means a positive $y$-coordinate.

17. What are the coordinates of a point that is $5$ units left and $7$ units down from the origin?

    $(-5, -7)$. Moving left from the origin gives a negative $x$-coordinate, and down gives a negative $y$-coordinate.

18. What is the name of the horizontal axis on a coordinate grid?

    $x$-axis. The horizontal axis runs left to right and is labeled as the $x$-axis in a coordinate plane.

19. Identify the coordinates of a point on the $x$-axis that is $12$ units left of the origin.

    $(-12, 0)$. Points on the $x$-axis have $y=0$, and left of the origin means a negative $x$-coordinate.

20. What is the coordinate of any point located on the $y$-axis (in terms of $x$)?

    $x = 0$. Any point on the $y$-axis has no horizontal displacement from the origin, so its $x$-coordinate is zero.

21. Which direction does the $x$-coordinate increase on a standard coordinate grid?

    To the right. Positive $x$-values increase as you move rightward from the origin along the $x$-axis.

22. What are the coordinates of the point that is $4$ units below the origin and on the $y$-axis?

    $(0, -4)$. Points on the $y$-axis have $x=0$, and below the origin means a negative $y$-coordinate.

23. Find and correct the ordered pair if a student wrote $(y, x)$ instead of $(x, y)$ for $x = 2$, $y = -9$.

    Correct ordered pair: $(2, -9)$. The standard ordered pair format requires $x$ first and $y$ second, so reversing the student's $(y, x)$ gives the correct pair.

24. What is the ordered pair format used to name a point on a coordinate grid?

    $(x, y)$. The ordered pair format specifies a point's position with the horizontal coordinate first and the vertical coordinate second on the grid.

25. What are the coordinates of a point that is $6$ units left and $2$ units up from the origin?

    $(-6, 2)$. Moving left from the origin gives a negative $x$-coordinate, and up gives a positive $y$-coordinate.

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