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AP EAMCET20224 Jul 2022Evening ShiftMathematicsStraight LinesActual

Suppose ∆ A B C is an isosceles triangle with ∠ C = 90 ° , A = 2 , 3 and B = 4 , 5 . Then the centroid of the triangle is

Options

  1. A13 8 , 8 3
  2. B11 3 , 10 3
  3. C10 3 , 13 3
  4. D10 3 , 11 3

Correct answer

D. 10 3 , 11 3

Step-by-step solution

Plotting the diagram of given value we have, So, A C = B C or A C 2 = B C 2 ⇒ x - 2 2 + y - 3 2 = x - 4 2 + y - 5 2 ⇒    4 - 4 x + 9 - 6 y = 16 - 8 x + 25 - 10 ⇒    4 x + 4 y = 28 ⇒    x + y = 7               . . . 1 Also A C ⊥ B C we get ⇒    Slope of A C × slope B C = - 1 3 - y 2 - x × 5 - y 4 - x = - 1             . . . 2 ⇒ 3 - y 5 - y = x - 4 2 - x ⇒

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