Question

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

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 $x_1=\frac{4}{5}$, $y_1=\frac{3}{5}$, $x_2 = 1$, $y_2=-2$.

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

First, find the x - coordinate: $\frac{\frac{4}{5}+1}{2}=\frac{\frac{4 + 5}{5}}{2}=\frac{\frac{9}{5}}{2}=\frac{9}{10}$.

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

Then, find the y - coordinate: $\frac{\frac{3}{5}-2}{2}=\frac{\frac{3-10}{5}}{2}=\frac{-\frac{7}{5}}{2}=-\frac{7}{10}$.

Answer:

$(\frac{9}{10},-\frac{7}{10})$