Question

find the cordinates of the point equidistant from three given pointsA(5,3)B(5,-5)C(1,-5).

Answer 1

Hey.... I think this can be ur answer dear!!
Let P (x,y) be the point...

SO, according to the question,
AP = BP
Squaring,
AP2= BP2
(5-x) 2 + (3-y)2 = (5-x)2 + (y+5) 2
(3-y)2 = (y+5)2
9 - 6y + y2 = y2 + 10y +25
9-25 = 10y +6y
-16 = 16y
y=-1....

Now,
BP =CP
Squaring,
BP2 = CP 2
(5-x)2 + (y+5)2 = (1-x)2 + (y+5)2
(5-x)2 = (1-x)2
25 - 10x + x2 = 1 - 2x + x2
25-1 = 10x-2x
8x=24
x=3....

So, coordinates of P are (3,-1)

Hope it helps you dear ☺️☺️☺️