if A(9,-9). (1. -3) are the end points of hypotenuse of a right angled isosceles triangle, then the third vertex
Answers
Given : A(9,-9). C (1. -3) are the end points of hypotenuse of a right angled isosceles triangle
To Find : the third vertex
Solution:
A(9,-9). C (1. -3) are the end points of hypotenuse of a right angled isosceles triangle
Hence median at hypotenuse will be perpendicular
Let say B = (x , y)
AB ⊥ BC
Slope of AB * Slope of BC = - 1
=> ( y + 9)/(x - 9) * ( y + 3)/(x - 1) = -1
=> y² + 12y + 27 = -(x² - 10x + 9)
=> x² + y² - 10x + 12y + 36 = 0
AB = BC given
=> (x - 9)² + (y +9)² = (x -1)² + (y + 3)²
=> x² - 18x + 81 + y²+ 18y + 81 = x² -2x + 1 + y² + 6y + 9
=> 16x - 12y = 152
=> 4x - 3y = 38
4x - 3y = 38
x² + y² - 10x + 12y + 36 = 0
on solving u get x = 2 and 8
third vertex ( 2 , - 10) or (8 , -2 )
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