Question

find the midpoint of the line segment whose end points are given. ($\frac{4}{5}$,$\frac{7}{2}$) and (1, - 2)
(-$\frac{1}{10}$,$\frac{11}{4}$)
($\frac{1}{10}$,-$\frac{11}{4}$)
($\frac{9}{5}$,$\frac{3}{2}$)
($\frac{9}{10}$,$\frac{3}{4}$)

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Here $x_1=\frac{4}{5}$, $y_1=\frac{7}{2}$, $x_2 = 1$, and $y_2=-2$.

Step2: Calculate the x - coordinate of the mid - point

$x=\frac{\frac{4}{5}+1}{2}=\frac{\frac{4 + 5}{5}}{2}=\frac{\frac{9}{5}}{2}=\frac{9}{10}$.

Step3: Calculate the y - coordinate of the mid - point

$y=\frac{\frac{7}{2}-2}{2}=\frac{\frac{7-4}{2}}{2}=\frac{\frac{3}{2}}{2}=\frac{3}{4}$.

Answer:

$(\frac{9}{10},\frac{3}{4})$