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Question

# Let the four vertices of a quadrilateral be A(−3,5), B(3,7), C(6,−2) and D(0,−4). Which of the following statements is/are true?

A
Length of one of the diagonals is 130 units
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B
Area of the quadrilateral is 60 sq. units
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C
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D
Both the diagonals of the quadrilateral are equal.
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Solution

## The correct option is D Both the diagonals of the quadrilateral are equal.A(−3,5),B(3,7),C(6,−2) and D(0,−4) Now, finding the distances, AB=√(−3−3)2+(5−7)2=√40 unitsBC=√(3−6)2+(7+2)2=√90 unitsCD=√(0−6)2+(−4+2)2=√40 unitsAD=√(−3−0)2+(5+4)2=√90 units As AB=CD and BC=AD Finding the diagonal length, AC=√(−3−6)2+(5+2)2=√130 unitsBD=√(0−3)2+(−4−7)2=√130 units Diagonal length is also same. Therefore it is a rectangle. Area of rectangle =√90×√40=60 sq. units

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