Question

if (x, y)is point of equidistan from the point A( 6, -1 )and B (2,3) show tha x-y=3​

Answer 1

ANSWER :

Let the point be P(x, y)

It is equidistant from A and B. Therefore the distance is same

ie, AP = BP

Squaring both sides(to eliminate the square root),

AP² = BP²

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

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

+ y²

37 - 13 - 12x + 4x + 2y + 6y + x² - x² + y² - y² = 0

24 - 8x + 8y = 0

24 = 8x - 8y

24 = 8(x - y)

x - y = 24/8

x - y = 3

Hence proved.

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