Question

If the point (x,y) be equidistant from the points (6,-1) and (2,3) such that Ax + By + C = 0, find the value of A + B + C + 10.

Answer 1

Answer:

Let the points be P(x,y), A(6,-1) and

B(2,3).

AP2 = (x-6)2 + (y+1)2

BP2 = (x-2)2 + (y-3)2

Given, 9(x,y) is equidistant from (6,-1) and (2,3)

(x-6)2 + (y+1)2 = (x-2)2 + (y-3)2

x2 - 12x + 36 + y2 + 2y + 1 = x2 - 4x + 4 + y2 - 6y + 9

-12x + 36 + 2y + 1 = - 4x + 4 - 6y + 9

-8x + 8y = -24

-x + y = -3

x - y = 3.

Step-by-step explanation:

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