Question

If $P\left(\frac{a}{3},4\right)$ is the midpoint of the line segment joining A(−6, 5) and B(−2, 3), then a = ?

(a) −4
(b) −12
(c) 12
(d) −6

Answer 1

(b) −12
The given points are A(−6, 5) and B(−2, 3).
Then, $\left(x_1=-6,y_1=5\right)\text{and}\left(x_2=-2,y_2=3\right)$
Therefore,
$$\begin{gathered} x=\frac{\left[\left(-6\right)+\left(-2\right)\right]}{2} \\ =\frac{-8}{2} \\ =-4 \end{gathered}$$
and
$$\begin{gathered} y=\frac{\left[5+3\right]}{2} \\ =\frac{8}{2} \\ =4 \end{gathered}$$
But the given midpoint is $P\left(\frac{a}{3},4\right)$ .
Therefore,
$$\begin{gathered} -4=\frac{a}{3} \\ \Rightarrow a=-12 \end{gathered}$$