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In this lesson, we will learn how to use the distance, slope, and midpoint formulas to determine whether a quadrilateral in the coordinate plane is a parallelogram.
Q1:
A parallelogram has vertices at the points π΄ , π΅ , πΆ , and π· with coordinates ( β 1 , 1 ) , ( 1 , 3 ) , ( 3 , β 1 ) , and ( 1 , β 3 ) respectively.
Work out the perimeter of the parallelogram π΄ π΅ πΆ π· . 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 π΄ π΅ πΆ π· .
Q2:
π΄ π΅ πΆ π· is a parallelogram. The coordinates of the points π΄ , π΅ , and πΆ are ( 0 , β 2 ) , ( 4 , 7 ) , and ( 6 , 3 ) respectively. Find the coordinates of π· .
Q3:
Calculate, to two decimal places, the area of the parallelogram π π π π , where the coordinates of its vertices are at π ( 2 , 1 , 3 ) , π ( 1 , 4 , 5 ) , π ( 2 , 5 , 3 ) , and π ( 3 , 2 , 1 ) .
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