# 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: **

Nabil 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?

- A6 by 2
- B7 by 2
- C1 by 2
- D7 by 6
- E1 by 6

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

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

**Q11: **

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

- A
- B
- C
- D
- E

**Q12: **

Amira 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 Amira 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.

- A12 length units, 25 area units
- B17 length units, 144 area units
- C5 length units, 169 area units
- D13 length units, 60 area units
- E length units, 34 area units