Question

Find the point on x-axis which is equidistant from the points A(2,-5) and B(-2,9)

Answer 1

Here, we need to find the point on X axis.

So, let the coordinate be P(x, 0)

According to the question,

$\bf{AP=PB}$

$\Rightarrow \: \sf{\sqrt{(x-2)^{2} + (0 - (-5))^{2} } = \sqrt{(-2-x)^{2} + (9 - 0)^{2} } }$

$\Rightarrow \: \sf{\sqrt{(x-2)^{2} + (5)^{2} } = \sqrt{(-2-x)^2 + (9)^{2} }}$

$\Rightarrow \: \sf{\sqrt{x^{2} + 4 - 4x + 25} = \sqrt{4 + x^{2} + 4x+ 81} }$

Cancelling square root on both sides,

→ x² - 4x + 29 = x² + 4x + 85

→ -4x + 29 = 4x + 85

→ 0 = 8x + 56

→ 8x = -56

∴ x = -7

So, the point on X axis is P(-7, 0)

Know more:

• Distance formula is used to find the distance between 2 points in co-ordinate geometry.
• Its formula is √(x₂ - x₁)² + (y₂ - y₁)²
• To divide a line segment in a particular ratio, we use section formula.