Question

Find the value of x if p(x 2) is equidistant from the point a(2 -1)and b(-4 5)

Answer 1

Answer:

x = -1

Step-by-step explanation:

p(x 2) is equidistant from the point a(2 -1)and b(-4 5)

Then pa = pb

$pa = \sqrt{(x-2)^{2} + (2 -(-1))^2}\\pa = \sqrt{(x-2)^2 + 3^2} \\pa = \sqrt{x^2 + 4 - 4x + 9} \\pa = \sqrt{x^2 -4x + 13}$

$pb = \sqrt{(x-(-4)^2 + (2-5)^2} \\pb = \sqrt{(x+4)^2 + (-3)^2} \\pb = \sqrt{x^2 + 16 + 8x + 9} \\pb =\sqrt{x^2 + 8x + 25}$

$\sqrt{x^2 -4x + 13} = \sqrt{x^2 + 8x + 25}\\x^2 - 4x + 13 = x^2 + 8x + 25\\-12x = 12\\x = -1$