Question

abc is a right angled triangle in which A (0-2),and B (2,0) are given .then find the coordinates of C

Answer 1

Answer:

C ( 0, 0 ) or ( 2, -2 )

Step-by-step explanation:

Given: ABC is Right Angled Triangle.

          Coordinates of A ( 0, -2 ) , B ( 2, 0 )

To find: Coordinates of C

Let ( x, y ) be coordinates of C,

And we assume C is right angle, so possible Figure is attached.

Then, from figure

BC will be perpendicular upon AC.

So,

Slope of BC × Slope of AC = -1

$\implies \frac{y-0}{x-2}\times\frac{y-(-2)}{x-0} = -1\\\\\implies \frac{y}{x-2}\times\frac{y+2}{x}=-1\\\\\implies \frac{y(y+2)}{x(x-2)}=-1\\\\\implies \frac{y^2+2y}{x^2-2x}=-1\\\\\implies y^2+2y=-(x^2-2x)\\\implies y^2+2y=-x^2+2x\\\implies y^2+2y+x^2-2x=0$

This only possible if x = 0 & y = 0 or x = 2 & y = -2

Therefore, C ( 0, 0 ) or ( 2, -2 )