Lesson Worksheet: Rectangles on the Coordinate Plane Mathematics • 6th Grade
In this worksheet, we will practice using the distance, slope, and midpoint formulas to determine the coordinates, area, and perimeter of a rectangle in the coordinate plane.
Q4:
Rectangle is graphed in the coordinate plane with its vertices at , and . Find its area.
Q6:
Given that the points , , , and are the vertices of the rectangle , determine the values of and .
- A,
- B,
- C,
- D,
- E,
Q7:
A parallelogram has vertices at the coordinates and .
Work out the length of the diagonal .
Work out the length of the diagonal .
- A
- B
- C
- D
- E
Using these lengths, is the parallelogram a rectangle?
- ANo
- BYes
Q8:
Given that the points , , and are the vertices of a right triangle at , find the coordinates of the point that make a rectangle.
- A
- B
- C
- D
Q9:
The coordinates of , , and are , , and respectively. Determine the coordinates of that would make a rectangle.
- A
- B
- C
- D
Q10:
Jacob has a rectangle-shaped garden which he wants to fence. He sketched his garden on a coordinate plane with vertices at , , , and .
What are the dimensions of his garden?
- A1 by 2
- B7 by 6
- C7 by 2
- D1 by 6
- E6 by 2
If each unit of the grid represents 1 m, how many meters of fencing should he buy?
Q11:
Select the expression that is equal to the area of the rectangle.
- A
- B
- C
- D
- E
Q13:
A quadrilateral has vertices at , , , and .
Decide if the quadrilateral is a parallelogram by calculating the length of each side.
- AIt is a parallelogram.
- BIt is not a parallelogram.
Decide if the quadrilateral is a rectangle by calculating the length of its diagonals.
- AIt is not a rectangle.
- BIt is a rectangle.
Q15:
A parallelogram has vertices , , , and .
Calculate the length of . Give an exact answer.
- A
- B
- C7
- D13
Calculate the length of . Give an exact answer.
- A
- B7
- C13
- D
Hence, state whether or not the parallelogram is a rectangle.
- AIt is a rectangle.
- BWe cannot decide without more information.
- CIt is not a rectangle.
Q17:
A quadrilateral has vertices at the points , , , and .
Work out the slope of the four edges of the quadrilateral.
- ASlope , slope , slope , slope
- BSlope , slope , slope , slope
- CSlope , slope , slope , slope
- DSlope , slope , slope , slope
- ESlope , slope , slope , slope
By finding the product of the slope, can we know if the quadrilateral is a rectangle?
- AYes
- BNo