Class 10

Math

All topics

Coordinate Geometry

Find the values of x for which the distance between the points $P(x,4)$ and $Q(9,10)$ is $10$ units.

Given: Points $P(x,4),Q(9,10)$ and $PQ=10$

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

$PQ_{2}=(x_{2}−x_{1})_{2}+(y_{2}−y_{1})_{2}$

$100=(9−x)_{2}+(10−4)_{2}$

$=81+x_{2}−18x+36$

$=117+x_{2}−18x$

$100=117+x_{2}−18x$

$x_{2}−18x+17x=0$ (solve this equation)

$(x−1)(x−17)$

$x=1$ or $x=17$.