# Worksheet: Rectangles in the Coordinate Plane

Q1:

A rectangle has vertices at the points , , , and with coordinates , , , and respectively.

Work out the perimeter of the rectangle . Give your solution to two decimal places.

Work out the area of the rectangle .

Q2:

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

Q3:

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

Q4:

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

Q5:

Given that the points , , , and are the vertices of the rectangle , determine the values of and .

• A ,
• B ,
• C ,
• D ,
• E ,

Q6:

The coordinates of , , and are , , and respectively. Determine the coordinates of that would make a rectangle.

• A
• B
• C
• D

Q7:

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

• A
• B
• C
• D
• E

Q8:

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?

• 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

Q9:

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

• A
• B
• C
• D
• E

Q10:

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

Q11:

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?

Q12:

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

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