Question

Show that the mid-point of the line segment joining the points $(5,7)$ and $(3,9)$ is also the mid-point of the line segment joining the points $(8,6)$ and $(0,10)$.

Answer 1

We have mid point formula,

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

So, Mid point of line joining the points (5,7) and (3,9) is

$\frac{5+3}{2},\frac{7+9}{2}$ $=(4,8)$-----(1)

As midpoint $(x_1,y_1)$ of line joining two points $(x_2,y_2)$ and $(x_3,y_3)$

$x_1=\frac{x_2+x_3}{2}$ and $y_1=\frac{y_2+y_3}{2}$

So midpoint of line joining two points $(8,6)$ and $(0,10)$

$\Rightarrow$ $\frac{8+0}{2},\frac{6+10}{2}$ $=(4,8)$-----(2)

From (1) and (2) we can say that the mid-point of the line segment joining the points(5,7) and(3,9) is also the mid-point of the line segment joining the points(8,6) and (0,10)

(0,10).