Question

If P(−1, 1) is the midpoint of the line segment joining A(−3, b) and B(1, b + 4), then b = ?

(a) 1
(b) −1
(c) 2
(d) 0

Answer 1

(b) −1
The given points are A(−3, b) and B(1, b+4).
Then, $\left(x_1=-3,y_1=b\right)\text{and}\left(x_2=1,y_2=b+4\right)$
Therefore,
$$\begin{gathered} x=\frac{\left[\left(-3\right)+1\right]}{2} \\ =\frac{-2}{2} \\ =-1 \end{gathered}$$
and
$$\begin{gathered} y=\frac{\left[b+\left(b+4\right)\right]}{2} \\ =\frac{2b+4}{2} \\ =b+2 \end{gathered}$$
But the midpoint is $P\left(-1,1\right)$.
Therefore,
$$\begin{gathered} b+2=1 \\ \Rightarrow b=-1 \end{gathered}$$