IF A(5,2) B(2,-2) and C(-2,t) are the vertices of a rightangled triang

1.	IF A(5,2) B(2,-2) and C(-2,t) are the vertices of a rightangled triangle with
Answer» 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 = 25BC2 = (- 2 - 2)2 + (t + 2)2 = 16 + (t + 2)2AC2 = (5 + 2)2\xa0+ (2 - t)2 = 49 + (2 - t)2Since {tex}\\triangle{/tex}ABC is a right angled triangle{tex}\\therefore{/tex}\xa0AC2 = AB2 + BC2or, 49 + (2 - t)2 = 25 + 16 + (t + 2)2or, 49 + 4 - 4t + t2 = 41 + t2\xa0+ 4t + 4or, 53 - 4t = 45 + 4tor, 8t = 8{tex}\\therefore{/tex}\xa0t =1

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