Question

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

Answer 1

Find the value of $a$ using distance formula

Distance between two points $(x_1,y_1)$and $(x_2,y_2)$ is given by distance formula

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

Let $A(–3,–14)=$$(x_1,y_1)$ and $B(a,–5)=$$(x_2,y_2)$

Distance between $A(–3,–14)$and $B(a,–5)$ is :

$d=\sqrt{{\left(a+3\right)}^2+{\left(-5+14\right)}^2}=9$

Squaring on L.H.S and R.H.S.

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

${\left(a+3\right)}^2=0$

$(a+3)(a+3)=0$

$a+3=0$

$a=-3$

Hence the value of $a$ is $-3$