Class 10

Math

All topics

Coordinate Geometry

Find the point on the x-axis which is equidistant from the points $(2,−5)$ and $(−2,9)$.

Let point $P(x,0)$ is on x-axis and equidustant from $A(2,−5)$ and $B(−2,9)$

$PA=PB$

or $PA_{2}=PB_{2}$

$(2−x)_{2}+(−5−0)_{2}=(−2−x)_{2}+(9−0)_{2}$

$(2−x)_{2}+(−5)_{2}=(−2−x)_{2}+(9)_{2}$

$29+x_{2}−4x=85+x_{2}+4x$

$56=−8x$

or $x=−7$

The point on x-axis is $(−7,0)$.