10th Class Mathematics Coordinate Geometry Question Bank Co-ordinate Geometry

  • question_answer Let\[\Delta \text{ABC}\]be a triangle whose vertices are (0, 0), (a, 5) and (-5, 5) respectively. If the triangle is right-angled at A, find the value of 'a'.

    A)  3                            

    B)         5

    C)  2                            

    D)         6

    Correct Answer: B

    Solution :

     Let A(0,0), B(a,5)and C(-5,5) be the vertices of the triangle. Therefore, \[\Delta \text{APB }\tilde{\ }\text{ }\Delta \text{DPC}\] \[\Rightarrow \] \[\frac{AP}{DP}=\frac{PB}{PC}=\frac{AB}{DC}\] \[\Rightarrow \] \[AP\times PC=PB\times DP\] \[\frac{1}{2}\sqrt{{{b}^{2}}+{{c}^{2}}}\times AD=\frac{1}{2}bc\] \[\Rightarrow \]\[AD=\frac{bc}{\sqrt{{{b}^{2}}+{{c}^{2}}}}\]

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