Question

use the midpoint formula to determine the midpoint of the given line segment. line segment (gh) with endpoints (g(-3\frac{1}{2}, - 1\frac{3}{4})) and (h(7,5)). enter the answer in each space provided. use numbers instead of words.

Explanation:

Step1: Convert mixed - numbers to improper fractions

$G(-3\frac{1}{2},-1\frac{3}{4})$ is $G(-\frac{7}{2},-\frac{7}{4})$ and $H(7,5)$. The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$.

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

$x=\frac{-\frac{7}{2}+7}{2}=\frac{-\frac{7}{2}+\frac{14}{2}}{2}=\frac{\frac{-7 + 14}{2}}{2}=\frac{\frac{7}{2}}{2}=\frac{7}{4}=1.75$

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

$y=\frac{-\frac{7}{4}+5}{2}=\frac{-\frac{7}{4}+\frac{20}{4}}{2}=\frac{\frac{-7 + 20}{4}}{2}=\frac{\frac{13}{4}}{2}=\frac{13}{8}=1.625$

Answer:

$(1.75,1.625)$