Question

The midpoint of the line segment joining the points A(−2, 8) and B(−6, −4) is

(a) (4, 2)
(b) (−4, 2)
(c) (2, 6)
(d) (−4, −6)

Answer 1

(b) (−4, 2)
The given points are A(−2, 8) and B(−6, −4).
Then, $\left(x_1=-2,y_1=8\right)\text{and}\left(x_2=-6,y_2=-4\right)$
Let M(x,y) be the midpoint of AB. Then,
$$\begin{gathered} x=\frac{\left[\left(-2\right)+\left(-6\right)\right]}{2} \\ =\frac{-8}{2} \\ =-4 \end{gathered}$$
and
$$\begin{gathered} y=\frac{\left[8+\left(-4\right)\right]}{2} \\ =\frac{4}{2} \\ =2 \end{gathered}$$
Hence, the required point is $M\left(-4,2\right)$.