Draw Polygons on Coordinate Plane - 6th Grade Math

1. Identify the error: A student says the length from $(2,1)$ to $(2,8)$ is $|2-2|=0$.

   Use $|8-1|$, so the length is $7$. Student used $x$-values instead of $y$-values for vertical segment.

2. What does the ordered pair $(x,y)$ represent on a coordinate plane?

   $x$ is horizontal, $y$ is vertical. First coordinate gives position left/right, second gives position up/down.

3. Identify whether the segment from $(-5,4)$ to $(3,4)$ is horizontal or vertical.

   Horizontal. Same $y$-coordinate ($y=4$) indicates horizontal line.

4. State the rule for the horizontal distance between $(x_1,y)$ and $(x_2,y)$.

   Distance $=|x_2-x_1|$. Absolute value ensures positive distance between $x$-coordinates.

5. What is the perimeter of the rectangle with vertices $ (0,0) $, $ (5,0) $, $ (5,3) $, $ (0,3) $?

   $16$. Rectangle has sides $5$ and $3$, so perimeter $=2(5+3)=16$.

6. A park path runs from $(0,2)$ to $(0,9)$ on a map where $1$ unit $=10$ m. What is its real length?

   $70$ m. Distance is $|9-2| = 7$ units; multiply by scale factor $10$.

7. What is the missing coordinate in $(4, )$ so that the point is directly above $(4,-2)$ by $7$ units?

   $5$. Add $7$ to $y=-2$: $-2+7=5$.

8. What is the distance between $(0,0)$ and $(0,7)$ on a coordinate plane?

   $7$. Vertical segment: $|7-0|=7$ units.

9. What is the length of the vertical segment from $(-1,6)$ to $(-1,2)$?

   $4$. Calculate $|2-6| = |-4| = 4$ since $x$-coordinates match.

10. Which coordinate stays the same for a horizontal side of a polygon: $x$ or $y$?

    $y$ stays the same. Horizontal means parallel to $x$-axis, so $y$ is constant.

11. What is the distance between $(6,-3)$ and $(1,-3)$ on a coordinate plane?

    $5$. Same $y$-coordinate means horizontal: $|6-1|=5$.

12. Find and correct the error: A student says the distance from $(2,3)$ to $(2,-1)$ is $-4$.

    Correct distance: $|{-1}-3|=4$. Distance must be positive; absolute value gives $4$, not $-4$.

13. What is the length of the vertical segment from $(3,-2)$ to $(3,5)$?

    $7$. Calculate $|5-(-2)| = |5+2| = 7$ since $x$-coordinates match.

14. What does the second coordinate $y$ tell you about a point on the coordinate plane?

    $y$ is the vertical position (up or down). The $y$-coordinate measures distance from the $x$-axis.

15. What is the length of the segment from $(0,0)$ to $(0,-9)$?

    $9$. Vertical segment: $|0-(-9)|=|0+9|=9$.

16. What is the name of the horizontal axis on a coordinate plane?

    The $x$-axis. The horizontal line through the origin where $y = 0$.

17. What is the length of the segment from $(3,-2)$ to $(3,6)$?

    $8$. Vertical segment: $|6-(-2)|=|6+2|=8$.

18. Identify the missing coordinate if a horizontal side goes from $(2,4)$ to $(7,\square)$.

    $4$. Horizontal segments require same $y$-coordinate throughout.

19. Identify which coordinate stays the same for a vertical segment on the coordinate plane.

    The $x$-coordinate stays the same. Points move only up/down when $x$ is constant.

20. What is the missing vertex of an axis-aligned rectangle with $(-3,2)$, $(4,2)$, $(-3,-1)$ given?

    $(4,-1)$. Fourth corner shares $x=4$ with $(4,2)$ and $y=-1$ with $(-3,-1)$.

21. State the rule for the length of a vertical segment from $(x,y_1)$ to $(x,y_2)$.

    Length $=|y_2-y_1|$. For vertical segments, subtract $y$-values and take absolute value.

22. What is the length of the segment from $(-5,4)$ to $(2,4)$?

    $7$. Horizontal segment: $|2-(-5)|=|2+5|=7$.

23. What is the area of the right triangle with vertices $(0,0)$, $(6,0)$, $(0,4)$?

    $12$. Right triangle area $=\frac{1}{2}×base×height=\frac{1}{2}×6×4=12$.

24. What is the ordered pair for a point with $x=-3$ and $y=5$?

    $(-3,5)$. Ordered pairs are written as $(x,y)$ with parentheses and comma.

25. What is the rule for a horizontal segment between $(x_1,y)$ and $(x_2,y)$?

    Same $y$; length is $|x_2-x_1|$. Horizontal segments have same $y$-coordinate; subtract $x$-values and take absolute value.

26. What does the ordered pair $(x,y)$ represent on the coordinate plane?

    $(x,y)$ means $x$ units right/left and $y$ units up/down. First coordinate shows horizontal position, second shows vertical position.

27. What is the length of the horizontal segment from $(-4,1)$ to $(2,1)$?

    $6$. Calculate $|2-(-4)| = |2+4| = 6$ since $y$-coordinates match.

28. What is the distance between $x=-2$ and $x=7$ on a coordinate line (a horizontal change)?

    $9$. Distance: $|7-(-2)|=|7+2|=9$.

29. Identify whether the segment from $(2,1)$ to $(2,7)$ is horizontal or vertical.

    Vertical. Same $x$-coordinate means the segment goes up/down.

30. What is the area of the rectangle with vertices $(1,1)$, $(6,1)$, $(6,4)$, $(1,4)$?

    $15$. Rectangle has width $5$ and height $3$, so area $=5×3=15$.

31. What is the area of the rectangle with vertices $(1,1)$, $(6,1)$, $(6,4)$, $(1,4)$?

    $15$. Area: length × width = $5×3=15$.

32. A map scale is $1$ unit $=2$ miles. Points are $(1,1)$ and $(1,6)$. What is the real distance?

    $10$ miles. Map distance is $5$ units; real distance $=5×2=10$ miles.

33. What is the missing vertex to complete a rectangle: $(2,1)$, $(6,1)$, $(6,5)$, $(\square,\square)$?

    $(2,5)$. Fourth corner shares $x$ with first point and $y$ with third point.

34. What is the distance between $(-4,1)$ and $(2,1)$ on a coordinate plane?

    $6$. Same $y$-coordinate means horizontal: $|2-(-4)|=6$.

35. What is the length of the horizontal segment from $(5,-3)$ to $(1,-3)$?

    $4$. Calculate $|1-5| = |-4| = 4$ since $y$-coordinates match.

36. What is the perimeter of the rectangle with vertices $(0,0)$, $(5,0)$, $(5,2)$, $(0,2)$?

    $14$. Add all four sides: $5+2+5+2 = 14$ units.

37. What is the perimeter of the square with vertices $(1,1)$, $(4,1)$, $(4,4)$, $(1,4)$?

    $12$. Four equal sides of length $3$: $4 \times 3 = 12$ units.

38. What is the name of the vertical axis on a coordinate plane?

    The $y$-axis. The vertical line through the origin where $x = 0$.

39. Identify whether the segment from $(-4,3)$ to $(5,3)$ is horizontal or vertical.

    Horizontal. Same $y$-coordinate means the segment goes left/right.

40. What is the rule for a vertical segment between $(x,y_1)$ and $(x,y_2)$?

    Same $x$; length is $|y_2-y_1|$. Vertical segments have same $x$-coordinate; subtract $y$-values and take absolute value.

41. What is the perimeter of the rectangle with vertices $(1,1)$, $(6,1)$, $(6,4)$, $(1,4)$?

    $16$. Perimeter: $2(5)+2(3)=10+6=16$.

42. Identify the missing coordinate if a vertical side goes from $(-3,1)$ to $(\square,6)$.

    $-3$. Vertical segments require same $x$-coordinate throughout.

43. Identify whether the segment from $(2,1)$ to $(2,9)$ is horizontal or vertical.

    Vertical. Same $x$-coordinate ($x=2$) indicates vertical line.

44. What is the distance between $(3,-2)$ and $(3,5)$ on a coordinate plane?

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

45. What is the perimeter of the square with vertices $(0,0)$, $(4,0)$, $(4,4)$, $(0,4)$?

    $16$. Square has side length $4$, so perimeter $=4×4=16$.

46. What is the side length of the square with vertices $(-2,-2)$, $(1,-2)$, $(1,1)$, $(-2,1)$?

    $3$. Distance between adjacent vertices: $|1-(-2)|=3$.

47. Which coordinate stays the same for a vertical side of a polygon: $x$ or $y$?

    $x$ stays the same. Vertical means parallel to $y$-axis, so $x$ is constant.

48. Identify which coordinate stays the same for a horizontal segment on the coordinate plane.

    The $y$-coordinate stays the same. Points move only left/right when $y$ is constant.

49. Identify the error: A student says length from $(3,2)$ to $(3,9)$ is $3-9=-6$.

    Use absolute value: $|9-2|=7$. Distance must be positive; absolute value ensures this.

50. What is the length of the segment from $(-6,1)$ to $(-1,1)$?

    $5$. Horizontal segment: $|-1-(-6)|=|-1+6|=5$.

51. What is the missing coordinate in $(,3)$ so that the point is $9$ units to the right of $(-2,3)$?

    $7$. Add $9$ to $x=-2$: $-2+9=7$.

52. State the rule for the vertical distance between $(x,y_1)$ and $(x,y_2)$.

    Distance $=|y_2-y_1|$. Absolute value ensures positive distance between $y$-coordinates.

53. What is the length of the vertical side of triangle with vertices $(2,1)$, $(2,8)$, $(7,1)$?

    $7$. Vertical side from $(2,1)$ to $(2,8)$ has length $|8-1|=7$.

54. State the rule for the length of a horizontal segment from $(x_1,y)$ to $(x_2,y)$.

    Length $=|x_2-x_1|$. For horizontal segments, subtract $x$-values and take absolute value.

55. What does the first coordinate $x$ tell you about a point on the coordinate plane?

    $x$ is the horizontal position (left or right). The $x$-coordinate measures distance from the $y$-axis.

56. What is the missing vertex of an axis-aligned rectangle with $(2,1)$, $(2,6)$, $(7,1)$ given?

    $(7,6)$. Fourth corner shares $x=7$ with $(7,1)$ and $y=6$ with $(2,6)$.

57. A park is a rectangle with corners $(0,0)$, $(0,8)$, $(5,8)$, $(5,0)$. What is its perimeter?

    $26$. Rectangle sides are $8$ and $5$, so perimeter $=2(8+5)=26$.

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