Question

Find the value of $y$ if the distance between the points $A(2,-3)$ & $B(10,y)$ is $10$ units.

Answer 1

$\text{Given}$ A$(2,-3)$ & B$(10,y)$ and AB $=10$ units

Distance between two points $=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$

$\therefore 10=\sqrt{{(10-2)}^2+{(y+3)}^2}$

Squaring both sides, we get

$\Rightarrow 100=8^2+y^2+6y+9$

$\Rightarrow y^2+6y-27=0$

$\Rightarrow$ $y^2+9y-3y-27=0$

$\Rightarrow y(y+9)-3(y+9)=0$

$\Rightarrow$ $(y+9)=0$ or $(y-3)=0$

$\Rightarrow y=-9$ or $y=3$

Therefore, $y=-9,3$