Question

find the midpoint of the line segment with endpoints $left(-\frac{7}{2},\frac{1}{2}
ight)$ and $left(-\frac{13}{2},-\frac{17}{2}
ight)$.

Explanation:

Step1: Recall mid - point formula

For two points $(x_1,y_1)$ and $(x_2,y_2)$, the mid - point $(x_m,y_m)$ is given by $x_m=\frac{x_1 + x_2}{2}$ and $y_m=\frac{y_1 + y_2}{2}$. Here $x_1=-\frac{7}{2}$, $y_1=\frac{1}{2}$, $x_2=-\frac{13}{2}$, $y_2=-\frac{17}{2}$.

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

$x_m=\frac{-\frac{7}{2}+(-\frac{13}{2})}{2}=\frac{-\frac{7 + 13}{2}}{2}=\frac{-\frac{20}{2}}{2}=\frac{-10}{2}=-5$.

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

$y_m=\frac{\frac{1}{2}+(-\frac{17}{2})}{2}=\frac{\frac{1-17}{2}}{2}=\frac{\frac{-16}{2}}{2}=\frac{-8}{2}=-4$.

Answer:

$(-5,-4)$