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The points A(1,-2) , B(2,3), C …

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The points A(1,-2) , B(2,3), C (k,2) and D(-4,-3) are the vertices of a parallelogram. Find the value of k.

Posted by Abhay Kumar Singh 6 years, 7 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 7 months ago

A(1, -2), B(2, 3), C(k, 2) and D(-4, -3)are the vertices of a parallelogram.
{tex}\Rightarrow{/tex}AB = CD and AD = BC
Consider AD = BC
{tex}\Rightarrow{/tex}AD²= BC²
{tex}\Rightarrow{/tex}(-4 -1)² + (-3 + 2)² = (k - 2)² + (2 - 3)²
{tex}\Rightarrow{/tex}(-5)² = (k - 2)²
{tex}\Rightarrow{/tex} k - 2 = -5
{tex}\Rightarrow{/tex} k = -3

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