Question

Find the point on x-axis which is equidistant from the points (2, –2) and

(–4, 2).​

Answer 1

☯ Explanation,

Let (a, 0) be the point on the x - axis that is equidistant from the points (2, -2) and (-4 , 2).

According to the question,

⇒ √(x - 2)² + (0 + 2)² = √(x + 4)² + (0 - 2)²

Squaring both sides, we get ;

⇒ (x - 2)² + (0 + 2)² = (x + 4)² + (0 - 2)²

⇒ x² - 4x + 4 + 4 = x² + 8x + 16 + 4

⇒ -4x + 8 = 8x + 20

⇒ -4x - 8x = 20 - 8

⇒ -12x = 12

⇒ x = -1

☯ Hence,

The required point on x - axis is (-1 , 0).

Answer 2

Let P(x,0) be a point on X-axis

PA = PB

PA2 = PB2

(x - 2)2 + (0 + 2)2 = (x + 4)2 + (0 - 2)2

x2 + 4 - 4x + 4

= x2 + 16 + 8x + 4

-4x + 4 = 8x + 16

x = -1

P(-1,0)