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Question

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

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Solution

## Find the value of $a$ using distance formulaDistance between two points $\left({x}_{1},{y}_{1}\right)$and $\left({x}_{2},{y}_{2}\right)$ is given by distance formula $d=\sqrt{{\left({x}_{2}-{x}_{1}\right)}^{2}+{\left({y}_{2}-{y}_{1}\right)}^{2}}$Let $A\left(–3,–14\right)=$$\left({x}_{1},{y}_{1}\right)$ and $B\left(a,–5\right)=$$\left({x}_{2},{y}_{2}\right)$Distance between $A\left(–3,–14\right)$and $B\left(a,–5\right)$ is :$d=\sqrt{{\left(a+3\right)}^{2}+{\left(-5+14\right)}^{2}}=9$ Squaring on L.H.S and R.H.S. ${\left(a+3\right)}^{2}+81=81$ ${\left(a+3\right)}^{2}=0$$\left(a+3\right)\left(a+3\right)=0$ $a+3=0$ $a=-3$Hence the value of $a$ is $-3$

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