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IF A(5,2) B(2,-2) and C(-2,t) are …

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IF A(5,2) B(2,-2) and C(-2,t) are the vertices of a rightangled triangle with <B=90° than find the value of 't'

Posted by Gopinath Messi 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

we are given that A (5, 2), B (2, - 2) and C (-2, t) are the vertices of a right-angled triangle with {tex}\angle B{/tex} = 90°.
AB² = ( 2 - 5)² + ( - 2 - 2)² =9 + 16 = 25
BC² = (- 2 - 2)² + (t + 2)² = 16 + (t + 2)²
AC² = (5 + 2)² + (2 - t)² = 49 + (2 - t)²
Since {tex}\triangle{/tex}ABC is a right angled triangle
{tex}\therefore{/tex} AC² = AB² + BC²
or, 49 + (2 - t)² = 25 + 16 + (t + 2)²
or, 49 + 4 - 4t + t² = 41 + t²+ 4t + 4
or, 53 - 4t = 45 + 4t
or, 8t = 8
{tex}\therefore{/tex} t =1

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