# Worksheet: Parallelograms on the Coordinate Plane

In this worksheet, we will practice using the distance, slope, and midpoint formulas to determine whether a quadrilateral in the coordinate plane is a parallelogram.

Q1:

The points , , , and are the vertices of quadrilateral . Using the slope formula, is the quadrilateral a parallelogram?

• Ayes
• Bno

Q2:

If is a quadrilateral, , , , and , find the midpoint of and , then determine what type of figure is.

• A , trapezium
• B , parallelogram
• C , parallelogram
• D , trapezium

Q3:

Where must the coordinates of point be so that is a parallelogram? In that case, what is the area of the parallelogram?

• A , area = 35
• B , area = 35
• C , area = 24
• D , area = 24

Q4:

If is a parallelogram, what can be said of the slope of line ?

• Athe slope of line = the slope of line
• Bthe slope of line = the slope of line
• Cthe slope of line = the slope of line
• Dthe slope of line = the slope of line

Q5:

is a parallelogram. The coordinates of the points , , and are , , and respectively. Find the coordinates of .

• A
• B
• C
• D

Q6:

Suppose that and fix two sides of a parallelogram. What is the area of this parallelogram, to the nearest hundredth?

Q7:

Given that , , and , determine the area of the parallelogram to the nearest hundredth.

Q8:

Determine, in square units, the area of the shown parallelogram.

Q9:

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

Work out the perimeter of the parallelogram . Give your solution to one decimal place.

By drawing a rectangle through the vertices of the parallelogram, or otherwise. Work out the area of the parallelogram .

Q10:

Calculate, to two decimal places, the area of the parallelogram , where the coordinates of its vertices are at , , , and .

Q11:

The points , , , and are the vertices of quadrilateral . Using the slope formula, is the quadrilateral a parallelogram?

• Ayes
• Bno

Q12:

Where must the coordinates of point be so that is a parallelogram? In that case, what is the area of the parallelogram?

• A , area = 36
• B , area = 36
• C , area = 24
• D , area = 24

Q13:

Where must the coordinates of point be so that is a parallelogram? In that case, what is the area of the parallelogram?

• A , area = 48
• B , area = 48
• C , area = 28
• D , area = 28

Q14:

If is a quadrilateral, , , , and , find the midpoint of and , then determine what type of figure is.

• A , trapezium
• B , parallelogram
• C , parallelogram
• D , trapezium

Q15:

A quadrilateral has vertices at the points and . What is the name of the quadrilateral?

• ARhombus
• BParallelogram
• CSquare
• DRectangle
• ETrapezoid