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If the vertex opposite to the hypotenuse of a right-angled triangle lies on the straight line 2 x + y - 10 = 0 and the two other vertices are 2 , - 3 and 4 , 1 , then the area of the triangle (in sq. units) is equal to

Options

  1. A10
  2. B3
  3. C33 5
  4. D11

Correct answer

B. 3

Step-by-step solution

m 1 m 2 = - 1 ⇒ 9 - 2 a a - 4 × 13 - 2 a a - 2 = - 1 ⇒ 5 a 2 - 50 a + 125 = 0 So, a = 5 and B is 5 , 0 Hence, required area = 1 2 A B × A C = 1 2 2 × 3 2 = 3 sq. units

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