Question

If P(a/3,4) is the mid point of the line segment joining the points Q(–6, 5) and R(–2, 3), then the value of 'a' is _________.

Answer 1

$\mathrm{Mid}\mathrm{point}\mathrm{of}\left(x_1,y_1\right)\mathrm{and}\left(x_2,y_2\right)\mathrm{is}\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right).$

P(a/3,4) is the mid point of the line segment joining the points Q(–6, 5) and R(–2, 3).

Therefore, using mid point formula the coordinates of P are:
$$\begin{gathered} \left(\frac{a}{3},4\right)=\left(\frac{-6-2}{2},\frac{5+3}{2}\right) \\ \Rightarrow \left(\frac{a}{3},4\right)=\left(\frac{-8}{2},\frac{8}{2}\right) \\ \Rightarrow \left(\frac{a}{3},4\right)=\left(-4,4\right) \\ \Rightarrow \frac{a}{3}=-4 \\ \Rightarrow a=-12 \end{gathered}$$

Hence, the value of 'a' is –12.