# 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