Question

Find the value of $a$, if the distance between the points $A(3,14)$ and $B(a,5)$ is $9$ units.

Answer 1

Given that - The line joining the points $A(x_1,y_1)=(3,14);B(x_2,y_2)=(a,5)$ is $9$ units long.

We apply the distance formula,

$AB=d=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$

$⟹9=\sqrt{{(a-3)}^2+{(5-14)}^2}$ units

on squaring both sides we get

$81=(a-3{)}^2+(5-14{)}^2$

$81=a^2+9-6a+25+196-140$

$0=a^2-6a+9$...(solve this quadratic equation and we get)

$⟹a=3$ units.