Question

13. (a) Let ABCD be a quadrilateral whose vertices are (6,8), (3,7), (-2,-2) and (1, -1) respectively.
Prove that ABCD is a parallelogram. Is it a rectangle?​

Answer 1

Given :  ABCD be a quadrilateral whose vertices are (6,8), (3,7), (-2,-2) and (1, -1) respectively.

To Find : Prove that ABCD is a parallelogram

Is it a rectangle?​

Solution:

A (6,8),   B (3,7),  C (-2,-2) and  D (1, -1)

Slope of AB  = ( 7 - 8)/(3 - 6)  =  1/3

Slope of CD  = ( -1 - (-2))/(1 -(-2))  = 1/3

Slope of AB = Slope of CD

=> AB  || CD

Slope of BC = 9/5

Slope of AD = 9/5

=> BC || AD

AB || CD & BC || AD

Hence ABCD is a parallogram

QED

Proved

Slope of AB * Slope of BC =  (1/3)(9/5)  = 3/5  ≠ - 1

Hence AB & BC are not perpendicular

so ABCD is not a rectangle

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Answer 2

Step-by-step explanation:

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