Find the value of a, if the distance between

Question:

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

Solution:

According to the question,

Distance between A (- 3, -14) and 8 (a, – 5), AB = 9

$\left[\because\right.$ distance between two points $\left(x_{1}, y_{1}\right)$ and $\left.\left(x_{2}, y_{2}\right), d=\sqrt{\left(x_{2}-x_{1}\right)+\left(y_{2}-y_{1}\right)^{2}}\right]$

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

$\Rightarrow \quad \sqrt{(a+3)^{2}+(9)^{2}}=9$

On squaring both the sides, we get

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

$\Rightarrow \quad(a+3)^{2}=0 \Rightarrow a=-3$

Hence, the required value of a is – 3.

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