Question

If the midpoint of the line segment joining the points $P(5,b-3)$ and $Q(3,4)$ is $(4,2)$ find the value of $b$.

Answer 1

We have the midpoint of the line segment joining the points $P(5,b-3)$ and $Q(3,4)$ is

$(\frac{5+3}{2},\frac{b-3+4}{2})$$=(4,\frac{b+1}{2})$.

According to the problem this mid-point is $(4,2)$.

Then we have,

$\frac{b+1}{2}=2$

or, $b+1=4$

or, $b=3$.