Class 10

Math

All topics

Coordinate Geometry

Find all possible values of x for which the distance between the points $A(x,−1)$ and $B(5,3)$ is $5$ units.

Given: Points $A(x,−1)$, $B(5,3)$ and $AB=5$ units

Distance formula: $AB=(x_{2}−x_{1})_{2}+(y_{2}−y_{1})_{2} $

$5=(5−x)_{2}+(3+1)_{2} $

Squaring both sides:

$25−10x+x_{2}+16=25$

$x_{2}−10x+16=0$

$x_{2}−2x−8x+16=0$

$x(x−2)−8(x−2)=0$

$(x−2)(x−8)=0$

Either $(x−2)=0$ or $(x−8)=0$

$x=2$ or $x=8$.