Question

the vertices of a triangle are a(0,2y) b(2x,0) c(0,0). then which is the point at equal distance from the three vertics pf this triangle.​

Answer 1

Point is (x , y)  equal distance from the three vertics of this triangle.​

Step-by-step explanation:

The vertices of a triangle are a(0,2y) b(2x,0) c(0,0)

Let say point  at equal distance from these three is P ( p , q)

Pa = Pb = Pc

=> Pa² = Pb² = Pc²

(p - 0)² + (q - 2y)²  =  (p - 2x)² + ( q - 0)² = (p - 0)² + (q - 0)²

=> p²  + q² + 4y² - 4qy  = p² + 4x² - 4px + q² = p²  + q²

Subtracting p²  + q² from all

=> 4y² - 4qy  =  4x² - 4px  = 0

4y² - 4qy  = 0

=> 4y - 4q = 0

=> q = y

4x² - 4px = 0

=> p = x

Point is (x , y)  equal distance from the three vertics of this triangle.​

Learn more:

Prove that the diagonals of a rectangle with vertices(0,0), (a,0), (a,b) and (0,b) bisect each other are equal

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