# Worksheet: Rectangles on 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.

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 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?

• 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:

William 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

Q12:

Given that is a rectangle, find the length of and the area of the rectangle. • A5 length units, 169 area units
• B17 length units, 144 area units
• C length units, 34 area units
• D12 length units, 25 area units
• E13 length units, 60 area units

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.

Q14:

A parallelogram has vertices at the coordinates and .

Work out the length of the diagonal .

Work out the length of the diagonal .

Using these lengths, is the parallelogram a rectangle?

• Ayes
• Bno

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.
• CIt is not a rectangle.

Q16:

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

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

Q18:

A quadrilateral has vertices at the points and . By determining the lengths of the quadrilateral’s sides, and considering the gradients of the intersecting lines, what is the name of the quadrilateral?

• Arectangle
• Brhombus
• Cparallelogram
• Dsquare
• Etrapezoid

Q19:

Name the polygon that can be graphed in the coordinate plane with vertices at , and .

• ASquare
• BRectangle
• CTriangle
• DRhombus