Question

If points A(5,p), B(1,5),C(2,1) and D(6,2) form a square ABCD then p=

Answer 1

Answer:

p = 2  or  p = -12

Step-by-step explanation:

A,B,C,D are points of a square

∴ All sides are equal

∴ Distance between AB = Distance between BC

Distance formula between two points (x1, y1) and (x2,y2) = √{(x2 - x1)² + (y2 - y1)²}

∴ √{(1 - 5)² + (5 - p)²} = √{(2 - 1)² + (1 - 5)²}

Taking square root on both the sides,

(-4)² + (5 - p)² = (1)² + (-4)²

16 + 25 - 10p - p² = 1 + 16

p² + 10p - 25 + 1 = 16 - 16

p² + 10p - 24 = 0

p² + 12p - 2p - 24 = 0

p (p + 12) - 2 (p + 12) = 0

(p - 2) (p + 12) = 0

p - 2 = 0  or p + 12 = 0

p = 2  or  p = -12