Question

Find the distance of the point (1, 2) from the midpoint of the line segment joining the points (6, 8) and (2, 4).

Answer 1

Let $C$ be the midpoint of the line segment joining $(6,8)$ and $(2,4)$.

We know that the coordinates of the midpoint of the line segment joining $(x_1,y_1)and(x_2,y_2)$ are:

$P(x,y)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Hence, coordinates of the $C$ will be:

$(\frac{6+2}{2},\frac{8+4}{2})=(4,6)$

We know that, the distance between two points $A(x_1,y_1)$ and $B(x_2,y_2)$ is $\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$

$\therefore$ Required distance between $C(4,6)\text{and}(1,2)=\sqrt{(4-1{)}^2+(6-2{)}^2}=\sqrt{9+16}=5units$

Hence, the distance between $(1,2)$ from the midpoint of the line segment joining $(6,8)$ and $(2,4)$ is $5units$.