Question

In the figure, calculate the distance from the midpoint to $\overline{EF}$ to the midpoint of $\overline{GH}$.

• A. $5.408$
• B. $5.454$
• C. $5.568$
• D. $5.590$
• E. $5.612$

Answer 1

The correct option is D $5.590$

Mid point of point $E(-3,3)$ and $F(-2,-4)$ is $\left(\frac{-3-2}{2}\right),\left(\frac{3-4}{2}\right)=\frac{-5}{2},\frac{-1}{2}=-2.5,-0.5$ ....(hint: using mid-point formula)

And mid point of $G(1,-2)$ and $H(5,3)$ is $\left(\frac{1+5}{2}\right),\left(\frac{3-2}{2}\right)=\frac{6}{2},\frac{1}{2}=3,0.5$

Then distance between mid point $EF$ to mid point $GH=$ $\sqrt{(-2.5-3{)}^2+(-0.5-0.5{)}^2}=\sqrt{(5.5{)}^2+(-1{)}^2}=\sqrt{30.25+1}=\sqrt{31.25}=5.590$