Question

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

Explanation:

Step1: Recall mid - point formula

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

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:

$(1.75,1.625)$