Question

Find the value of $x_1$ if the distance between the points $(x_1,2)$ and $(3,4)$ be $8$.

Answer 1

Distance between points $(x_1,y_1)$ and $(x_2,y_2)$ is $\sqrt{(x_1-x_2{)}^2+(y_1-y_2{)}^2}$

Let $P(x_1,2)$ and $Q(3,4)$

Given : $PQ=8$

$\Rightarrow \sqrt{{(3-x_1)}^2+{(4-2)}^2}=8$

Squaring both sides, we get

${(3-x_1)}^2+{(4-2)}^2=64{(3-x_1)}^2+4=64{(3-x_1)}^2=60{(x_1-3)}^2=60$

Taking square root on both sides

$x_1-3=\pm 2\sqrt{15}{x}_1=3\pm 2\sqrt{15}$