Question

Kindly solve fast...​

Answer 1

Took a while, hope it helps.

To Find : coordinates of  C

Solution:

ACB is a right angle triangle at C  and  isosceles triangle

Hence AC = BC

A = ( - 1, -7)

B = (-7 , - 1)

Let say C = ( x, y)

AC & CB are perpendicular to each other

Hence slope of AC * Slope of BC = - 1

=> ( y + 7)/(x + 1)   *  ( y + 1)/(x + 7) = - 1

=> y² + 8y + 7 =  -x² - 8x - 7

=> x² + y²  + 8x + 8y  + 14 = 0

AC² = (x + 1)² + (y + 7)²

BC² = (x + 7)² + (y + 1)²

AC = BC

=> AC² = BC²

=> (x + 1)² + (y + 7)² = (x + 7)² + (y + 1)²

=> x² + 2x + 1 + y² + 49 + 14y  = x² + 14x + 49 + y² + 1 + 2y

=> 12y = 12x

=> x = y

x² + y²  + 8x + 8y  + 14 = 0

=> x² + x²  + 8x + 8x  + 14 = 0

=> x² + 8x + 7 = 0

=> (x + 7)(x + 1) = 0

=> x = - 7 , - 1

=> y = -7 ,   - 1

Hence C  is ( -7 , -7)  or  (-1, - 1)

Coordinates of  third vertex of the triangle   ( -7 , -7)  or  (-1, - 1)

Take care : ))

Answer 2

Step-by-step explanation:

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