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In this lesson, we will learn how to identify quadrilaterals described by the coordinates of their vertices by calculating slopes and lengths of sides and diagonals.

Q1:

Consider quadrilateral π΄ π΅ πΆ π· with vertices π΄ ( β 2 , 4 ) , π΅ ( β 4 , 4 ) , πΆ ( β 1 , β 5 ) , and π· ( 1 , β 5 ) . Using the distance formula, determine whether the quadrilateral is a parallelogram.

Q2:

Consider quadrilateral π΄ π΅ πΆ π· with vertices π΄ ( 5 , 4 ) , π΅ ( 3 , 5 ) , πΆ ( β 1 , β 5 ) , and π· ( β 3 , β 6 ) . Using the distance formula, determine whether the quadrilateral is a parallelogram.

Q3:

Consider quadrilateral π΄ π΅ πΆ π· with vertices π΄ ( 2 , 2 ) , π΅ ( 5 , 3 ) , πΆ ( 2 , β 1 ) , and π· ( β 1 , β 2 ) . Using the distance formula, determine whether the quadrilateral is a parallelogram.

Q4:

Quadrilateral π΄ π΅ πΆ π· has vertices π΄ ( β 1 , 7 ) , π΅ ( 4 , 4 ) , πΆ ( 3 , β 3 ) , and π· ( β 2 , 0 ) . Using the midpoint formula, determine whether π΄ π΅ πΆ π· is a parallelogram.

Q5:

Quadrilateral π΄ π΅ πΆ π· has vertices π΄ ( β 1 , 7 ) , π΅ ( 4 , 4 ) , πΆ ( 3 , β 3 ) , and π· ( 8 , 6 ) . Using the midpoint formula, determine whether π΄ π΅ πΆ π· is a parallelogram.

Q6:

Find the area of a quadrilateral with vertices π΄ ( β 1 2 , β 5 ) , π΅ ( β 9 , β 9 ) , πΆ ( β 4 , β 9 ) , and π· ( β 7 , β 5 ) .

Q7:

Find the perimeter and the area of the quadrilateral whose vertices are π ( 4 , β 2 ) , π ( 1 0 , 4 ) , π ( 1 4 , 0 ) , and π ( 8 , β 6 ) . If necessary, round your answers to the nearest tenth.

Q8:

Find the perimeter and area of the quadrilateral whose vertices are π ( β 4 , 0 ) , π ( 5 , 1 2 ) , π ( 1 7 , 3 ) , and π ( 8 , β 9 ) .

Q9:

A quadrilateral has vertices at the points π΄ ( 0 , 5 ) , π΅ ( 2 , 6 ) , πΆ ( 4 , 2 ) , and π· ( 2 , 1 ) .

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

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

Q10:

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 ( 1 0 , 6 0 ) , ( 7 0 , 6 0 ) , ( 5 0 , 2 0 ) , and ( 1 0 , 2 0 ) . Find the area of the lion's enclosure.

Q11:

A quadrilateral has vertices at the points π΄ ( 0 , 5 ) , π΅ ( 1 , 7 ) , πΆ ( 4 , 5 ) , and π· ( 2 , 1 ) .

What type of shape is π΄ π΅ πΆ π· ?

Q12:

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 ( 2 0 , 1 0 ) , ( 2 0 , 5 0 ) , ( 5 0 , 5 0 ) , ( 7 0 , 7 0 ) , and ( 7 0 , 1 0 ) . Find the area of the building.

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