Quadrilateral EFGH has vertices at E(3,6), F(5,7), G(6,5), and H(3,2).Is EFGH a kite? Why or why not?
Question
Quadrilateral EFGH has vertices at E(3,6), F(5,7), G(6,5), and H(3,2).Is EFGH a kite? Why or why not?
Solution
A quadrilateral is a kite if it has two pairs of adjacent sides that are equal in length.
Step 1: Calculate the lengths of all sides of the quadrilateral EFGH.
The distance between two points (x1, y1) and (x2, y2) can be calculated using the distance formula: √[(x2-x1)² + (y2-y1)²].
EF = √[(5-3)² + (7-6)²] = √[4 + 1] = √5 FG = √[(6-5)² + (5-7)²] = √[1 + 4] = √5 GH = √[(3-6)² + (2-5)²] = √[9 + 9] = √18 HE = √[(3-3)² + (6-2)²] = √[0 + 16] = √16 = 4
Step 2: Check if there are two pairs of adjacent sides that are equal in length.
EF = FG = √5 and GH = HE = 4
So, EFGH has two pairs of adjacent sides that are equal in length.
Therefore, EFGH is a kite.
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