Question

If the middle point of two points A(-2, 5) and B(-5, y) is $(\frac{-7}{2},3)$, then find the distance between points A and B.

Answer 1

Let the middle point be $P$

Using distance formula,

$AP=\sqrt{{(-\frac{7}{2}-(-2\left)\right)}^2+{(3-5)}^2}$

$AP=\sqrt{\frac{9}{4}+4}$

$AP=\frac{5}{2}$

$AB=2AP$ as $P$ is the mid point of $AB$

$AB=5$.