# Worksheet: Quadrilaterals on the Coordinate Plane

In this worksheet, we will practice identifying quadrilaterals described by the coordinates of their vertices by calculating slopes and lengths of sides and diagonals.

Q1:

Consider quadrilateral with vertices , , , and . Using the distance formula, determine whether the quadrilateral is a parallelogram.

• Ayes
• Bno

Q2:

Quadrilateral has vertices , , , and . Using the midpoint formula, determine whether is a parallelogram.

• AIt is a parallelogram.
• BIt is not a parallelogram.

Q3:

A quadrilateral has vertices at the points and .

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

• A Slope
• B Slope
• C Slope
• D Slope
• E Slope

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

• Ayes
• Bno

Q4:

A quadrilateral has vertices at the points and .

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

• A Slope of , Slope of , Slope of , Slope of
• B Slope of , Slope of , Slope of , Slope of
• C Slope of , Slope of , Slope of , Slope of
• D Slope of , Slope of , Slope of , Slope of
• E Slope of , Slope of , Slope of , Slope of

What type of shape is ?

• Atrapezium
• Bsquare
• Crectangle
• Dparallelogram
• Erhombus

Q5:

Find the perimeter and area of the quadrilateral whose vertices are , , , and .

• Aperimeter , area
• Bperimeter , area
• Cperimeter , area
• Dperimeter , area
• Eperimeter , area

Q6:

Find the perimeter and the area of the quadrilateral whose vertices are , , , and . If necessary, round your answers to the nearest tenth.

• Aperimeter , area
• Bperimeter , area
• Cperimeter , area
• Dperimeter , area
• Eperimeter , area

Q7:

Find the area of a quadrilateral with vertices , , , and .

Q8:

A zoo plotted a map of its exhibits on the coordinate plane where each unit represented 1 ft. The vertices of the lion's enclosure were at , , , and . Find the area of the lion's enclosure.

Q9:

A factory plotted its building on a map using a coordinate plane where each unit represented 1 m. The vertices of one of the buildings were plotted at , , , , and . Find the area of the building.

Q10:

Consider quadrilateral with vertices , , , and . Using the distance formula, determine whether the quadrilateral is a parallelogram.

• Ano
• Byes

Q11:

Consider quadrilateral with vertices , , , and . Using the distance formula, determine whether the quadrilateral is a parallelogram.

• Ayes
• Bno

Q12:

Quadrilateral has vertices , , , and . Using the midpoint formula, determine whether is a parallelogram.

• AIt is not a parallelogram.
• BIt is a parallelogram.

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