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Question

Show that four points (0, – 1), (6, 7), (–2, 3) and (8, 3) are the vertices of a rectangle. Also, find its area. [3 MARKS]

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Solution

Formula: 1 Mark
Application: 1 Mark
Answer: 1 Mark

Let A (0 , -1) , B (6 , 7) , C ( -2 ,3) and D (8 , 3) be the given points. Then,

AB=(60)2+(7+1)2=36+64=10

CD=(8+2)2+(33)2=100+0=10

AD=(80)2+(3+1)2=64+16=45

BC=(6+2)2+(73)2=64+16=45

AB = CD and AD = BC

So, ABCD is a parallelogram

Now , AC=(20)2+(3(1)2=4+16=25

and , BD=(86)2+(37)2=4+16=25

Clearly, opposite sides are equal and diagonals are equal
.
Hence, ABCD is a rectangle.

Now, Area of rectangle ABCD=AB×BC

AB×BC=10×45 sq.units

AB×BC=405 sq.units


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