Question

Find the equations of the sides of a right-angled isosceles triangle whose hypotenuse is the line 3x + 4y + 4 = 0 and the right angle vertex is the point (2, 2). 

Answer 1

See Fig. Let the slope of AB be m. Therefore

Two cases arise:

Case 1:  4m + 3 = 3m - 4 ⇒ m = -7.

Case 2:  4m + 3 = -(3m - 4) ⇒ m = 1/7.

Therefore, the equations of the sides AB and AC are

y - 2 = -7(x - 2) ⇒ 7x + y - 16 = 0

and  y - 2 = 1/7(x - 2) ⇒ x - 7y + 12 = 0