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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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