Graph Points in Four Quadrants - 6th Grade Math

1. What is the distance between $(-3,4)$ and $(6,4)$?

   $9$. Same $y$-coordinate means horizontal distance: $|6-(-3)|=|9|=9$.

2. State the distance formula for points with the same $y$-coordinate: $(x_1, y)$ and $(x_2, y)$.

   $|x_2 - x_1|$. For horizontal alignment, distance is the absolute difference of $x$-values.

3. Which quadrant contains points with $x<0$ and $y<0$?

   Quadrant III. Both coordinates are negative in the lower-left region.

4. State the distance formula for points with the same $x$-coordinate: $(x, y_1)$ and $(x, y_2)$.

   $|y_2 - y_1|$. For vertical alignment, distance is the absolute difference of $y$-values.

5. Which quadrant contains points where $x < 0$ and $y > 0$?

   Quadrant $II$. Negative $x$ and positive $y$ defines the upper-left quadrant.

6. Which quadrant contains points where $x<0$ and $y>0$?

   Quadrant $II$. Negative x (left) and positive y (up) defines Quadrant II.

7. What is the distance between $(7, 3)$ and $(-1, 3)$?

   $8$. Same $y$-coordinate: $|-1 - 7| = |-8| = 8$.

8. What ordered pair names the point with $x=-3$ and $y=5$?

   $(-3,5)$. The ordered pair format is $(x,y)$ with $x$ first, then $y$.

9. What do the coordinates $(x,y)$ represent on the coordinate plane?

   $x$ is horizontal, $y$ is vertical. The first coordinate measures left/right, the second measures up/down.

10. Which axis is the $y$-axis: horizontal or vertical?

    Vertical. The $y$-axis runs up-down on the plane.

11. What is the ordered pair for a point that is $4$ units left and $5$ units down from the origin?

    $(-4, -5)$. Left means negative $x$, down means negative $y$.

12. Which coordinate is the $x$-coordinate in an ordered pair $(x, y)$: first or second?

    First coordinate. In $(x, y)$, $x$ comes first, then $y$.

13. Identify the quadrant (or axis) for the point $(2, -7)$.

    Quadrant $IV$. Positive $x$ and negative $y$ places it in the lower-right.

14. Which quadrant contains points with $x>0$ and $y<0$?

    Quadrant IV. Positive $x$ and negative $y$ place points in the lower-right region.

15. Identify the correct expression for the distance between $(4, -1)$ and $(4, 6)$.

    $|6-(-1)|$. Vertical points: use absolute value of y-coordinates.

16. What is the distance between $(-5, -2)$ and $(3, -2)$?

    $8$. Same y-coordinate: distance = $|3-(-5)| = 8$.

17. What is the distance between $(2, 1)$ and $(2, 7)$?

    $6$. Same x-coordinate: distance = $|7-1| = 6$.

18. What is the $y$-axis: the set of points where $x = 0$ or where $y = 0$?

    Points where $x = 0$. The vertical axis contains all points with zero $x$-value.

19. Which quadrant contains points where $x>0$ and $y<0$?

    Quadrant $IV$. Positive x (right) and negative y (down) defines Quadrant IV.

20. What are the coordinates of a point $3$ units right and $2$ units up from the origin?

    $(3, 2)$. Move right along x-axis and up along y-axis from origin.

21. Which quadrant contains points where $x > 0$ and $y < 0$?

    Quadrant $IV$. Positive $x$ and negative $y$ defines the lower-right quadrant.

22. Identify the quadrant of the point $(6,-1)$.

    Quadrant IV. Positive $x$ and negative $y$ place the point in the lower-right quadrant.

23. Find the distance between $(-8,3)$ and $(-2,3)$.

    $6$. Same $y$-coordinate: $|-2-(-8)|=|6|=6$.

24. What is the distance between $(-3, 6)$ and $(5, 6)$?

    $8$. Same $y$-coordinate: $|5 - (-3)| = |8| = 8$.

25. Identify the quadrant of the point $(-4,2)$.

    Quadrant II. Negative $x$ and positive $y$ place the point in the upper-left quadrant.

26. What is the ordered pair for a point that is $3$ units right and $2$ units up from the origin?

    $(3, 2)$. Right means positive $x$, up means positive $y$.

27. What is the distance between $(0, -4)$ and $(0, 9)$?

    $13$. Same x-coordinate: distance = $|9-(-4)| = 13$.

28. What is the distance between $(-2, -1)$ and $(-2, -9)$?

    $8$. Same $x$-coordinate: $|-9 - (-1)| = |-8| = 8$.

29. What is the $x$-axis: the set of points where $y = 0$ or where $x = 0$?

    Points where $y = 0$. The horizontal axis contains all points with zero $y$-value.

30. What is the quadrant of the point $(4, -3)$?

    Quadrant $IV$. Quadrant IV has positive x and negative y values.

31. Which quadrant contains points with $x>0$ and $y>0$?

    Quadrant I. Both coordinates are positive in the upper-right region.

32. Which quadrant contains points with $x<0$ and $y>0$?

    Quadrant II. Negative $x$ and positive $y$ place points in the upper-left region.

33. What is the value of the absolute value expression $|-12|$?

    $12$. Absolute value makes negative numbers positive.

34. Identify the location for the point $(7, 0)$: $x$-axis, $y$-axis, or a quadrant.

    $x$-axis. When $y = 0$, the point lies on the horizontal axis.

35. Identify the axis a point lies on when its $x$-coordinate is $0$.

    The $y$-axis. Points with x = 0 lie on the vertical axis.

36. State the distance formula for points with the same $x$-coordinate: $(a,y_1)$ and $(a,y_2)$.

    Distance $=|y_2-y_1|$. For vertical alignment, find the absolute difference of $y$-values.

37. What are the coordinates of a point $4$ units left and $5$ units down from the origin?

    $(-4, -5)$. Negative coordinates mean left (x) and down (y) from origin.

38. State the distance formula for points with the same $y$-coordinate: $(x_1,b)$ and $(x_2,b)$.

    Distance $=|x_2-x_1|$. For horizontal alignment, find the absolute difference of $x$-values.

39. Identify the axis a point lies on when its $y$-coordinate is $0$.

    The $x$-axis. Points with y = 0 lie on the horizontal axis.

40. Identify the quadrant (or axis) for the point $(-3, -4)$.

    Quadrant $III$. Both coordinates negative places it in the lower-left.

41. Identify the quadrant (or axis) for the point $(5, 9)$.

    Quadrant $I$. Both coordinates positive places it in the upper-right.

42. What is the distance between $(2,-1)$ and $(2,5)$?

    $6$. Same $x$-coordinate means vertical distance: $|5-(-1)|=|6|=6$.

43. What is the distance between $(9, -3)$ and $(9, -10)$?

    $7$. Same x-coordinate: distance = $|-3-(-10)| = 7$.

44. What is the absolute value of $-9$, and what does it represent on a number line?

    $9$; distance from $0$. Absolute value removes the negative sign, measuring distance from zero.

45. What is the quadrant of the point $(-6, 2)$?

    Quadrant $II$. Quadrant II has negative x and positive y values.

46. What is the distance between $(4, -2)$ and $(4, 5)$?

    $7$. Same $x$-coordinate: $|5 - (-2)| = |7| = 7$.

47. Identify the location for the point $(0, -8)$: $x$-axis, $y$-axis, or a quadrant.

    $y$-axis. When $x = 0$, the point lies on the vertical axis.

48. Identify the quadrant of the point $(-2,-7)$.

    Quadrant III. Both coordinates are negative, placing the point in the lower-left quadrant.

49. Find the distance between $(0,-6)$ and $(0,1)$.

    $7$. Same $x$-coordinate: $|1-(-6)|=|7|=7$.

50. Identify the quadrant (or axis) for the point $(-6, 1)$.

    Quadrant $II$. Negative $x$ and positive $y$ places it in the upper-left.

51. What is the name of the point where the axes intersect?

    The origin, $(0,0)$. Both coordinates equal zero at the axes' intersection.

52. Which axis is the $x$-axis: horizontal or vertical?

    Horizontal. The $x$-axis runs left-right across the plane.

53. Identify the correct expression for the distance between $(-3, 2)$ and $(5, 2)$.

    $|5-(-3)|$. Horizontal points: use absolute value of x-coordinates.

54. What is the distance between $(-7, 5)$ and $(1, 5)$?

    $8$. Same y-coordinate: distance = $|1-(-7)| = 8$.

55. Identify the quadrant of the point $(3,9)$.

    Quadrant I. Both coordinates are positive, placing the point in the upper-right quadrant.

56. What is the quadrant of the point $(-1, -8)$?

    Quadrant $III$. Quadrant III has both negative x and y values.

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