Question

what is the slope of the line that connects point o with the mid - point of mn? record the answer as a fraction in lowest terms.

Explanation:

Step1: Find the mid - point of MN

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Given $M(-7,-4)$ and $N(7,0)$, then the mid - point $P$ of $MN$ has coordinates $(\frac{-7 + 7}{2},\frac{-4+0}{2})=(0,-2)$.

Step2: Calculate the slope between O and the mid - point

The slope formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Given $O(4,5)$ and $P(0,-2)$, then $m=\frac{5-(-2)}{4 - 0}=\frac{5 + 2}{4}=\frac{7}{4}$.

Answer:

$\frac{7}{4}$