# Worksheet: Rectangles in the Coordinate Plane

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.

**Q2: **

Rectangle is graphed in the coordinate plane with its vertices at , and . Find its perimeter.

**Q3: **

Rectangle is graphed in the coordinate plane with its vertices at , and . Find its area.

**Q4: **

Rectangle is graphed in the coordinate plane with its vertices at , and . Find its area.

**Q5: **

Rectangle is graphed in the coordinate plane with vertices , , and . Find the coordinates of point .

- A
- B
- C
- D
- E

**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?

- Ayes
- Bno

**Q8: **

Given that the points , , and are the vertices of a right-angled 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: **

William has a rectangle-shaped garden which he wants to fence. He sketched his garden on a coordinate plane with vertices at , (4,3), , and

What are the dimensions of his garden?

- A7 by 6
- B6 by 2
- C1 by 6
- D1 by 2
- E7 by 2

If each unit of the grid represents 1 m, how many meters of fencing should he buy?

- A 14 m
- B 16 m
- C 26 m
- D 18 m
- E 6 m

**Q11: **

Select the expression that is equal to the area of the rectangle.

- A
- B
- C
- D
- E

**Q12: **

Sophia drew plans for her living room. She connected the following points, on grid paper, in order: , , , , , , and . If the side length of each grid square represents 3 feet of the room, and Sophia wants to carpet the room, how many square feet will she need to carpet?

**Q13: **

Given that is a rectangle, find the length of and the area of the rectangle.

- A length units, 34 area units
- B5 length units, 169 area units
- C12 length units, 25 area units
- D13 length units, 60 area units
- E17 length units, 144 area units

**Q14: **

A quadrilateral has vertices at , , , and .

Decide if the quadrilateral is a parallelogram by calculating the length of each side.

- AIt is not a parallelogram.
- BIt is a parallelogram.

Decide if the quadrilateral is a rectangle by calculating the length of its diagonals.

- AIt is a rectangle.
- BIt is not a rectangle.

**Q16: **

A parallelogram has vertices , , , and .

Calculate the length of . Give an exact answer.

- A
- B13
- C7
- D

Calculate the length of . Give an exact answer.

- A13
- B
- C
- D7

Hence, state whether or not the parallelogram is a rectangle.

- AWe cannot decide without more information.
- BIt is not a rectangle.
- CIt is a rectangle.

**Q17: **

A parallelogram has vertices at the coordinates and .

Work out the slope of .

Work out the slope of .

Work out the product of the slopes from parts (a) and (b).

Is a rectangle?

- Ano
- Byes

**Q18: **

A quadrilateral has vertices at the points , , , and .

Work out the slope of the four edges of the quadrilateral.

- A Slope , slope , slope , slope
- B Slope , slope , slope , slope
- C Slope , slope , slope , slope
- D Slope , slope , slope , slope
- E Slope , slope , slope , slope

By finding the product of the slope, can we know if the quadrilateral is a rectangle?

- ANo
- BYes