Question

Find the coordinates of the midpoint of the line joining the points $(-3,10)$ and $(6,-8)$.

Answer 1

We know that the mid point formula $M=(x,y)$ of the two points $(x_1,y_1)$ and $(x_2,y_2)$ is:

$(x,y)=(\frac{x_1{+x}_2}{2},\frac{y_1{+y}_2}{2})$

Here, the given points are $(-3,10)$ and $(6,-8)$, therefore,

$(x,y)=(\frac{x_1{+x}_2}{2},\frac{y_1{+y}_2}{2})\Rightarrow (x,y)=(\frac{-3+6}{2},\frac{10+(-8)}{2})\Rightarrow (x,y)=(\frac{3}{2},\frac{10-8}{2})\Rightarrow (x,y)=(\frac{3}{2},\frac{2}{2})\Rightarrow (x,y)=(\frac{3}{2},1)$

Hence, the coordinates of the mid point are $(\frac{3}{2},1)$.