Question

32, Find the coordinates of the point which is equidistant from the three vertices
A (2x, 0), O (0,0) and B (0,2y) of A AOB.

Answer 1

Answer:

( x,y)

Step-by-step explanation:

let the point be ( a,b)

(a-2x)² + b² = a² + (b-2y)² = a²+b²

a²+b² + 4x² - 4ax = a²+b² + 4y² - 4by ,

x² - ax + a²/4 +b²/4 =  y² - 4by a²/4 +b²/4

(x-a/2)² + b²/4 = (y-b/2)² + a²/4

a²+b² = (2x-a)² + b², 2x-a = ±a

 2x-a = ±a

2y-b = ±b

±a + a = 2x

±b + b = 2y

therefore

a = x , b = y

( a,b) =  ( x,y)