Question

If the distance between the points A(–3, –14) and B(a, –5) is 9 units, then a = __________.

Answer 1

The distance between $\left(x_1,y_1\right)\mathrm{and}\left(x_2,y_2\right)\mathrm{is}\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}$.

Therefore, the distance between the points A(–3, –14) and B(a, –5)$=\sqrt{{\left(a-\left(-3\right)\right)}^2+{\left(-5-\left(-14\right)\right)}^2}$
$$\begin{gathered} \Rightarrow 9=\sqrt{{\left(a+3\right)}^2+{\left(-5+14\right)}^2} \\ \mathrm{Squaring}\mathrm{both}\mathrm{sides},\mathrm{we}\mathrm{get} \\ \Rightarrow {\left(9\right)}^2={\left(\sqrt{{\left(a+3\right)}^2+{\left(9\right)}^2}\right)}^2 \\ \Rightarrow 81={\left(a+3\right)}^2+81 \\ \Rightarrow {\left(a+3\right)}^2=0 \\ \Rightarrow a=-3 \end{gathered}$$

Hence, a = –3.