Question

show mathematically that (1, 5.5) is the midpoint of the line segment with endpoints (-2, 1) and (4, 10).

Explanation:

Step1: Recall mid - point formula

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

Let $(x_1,y_1)=(-2,1)$ and $(x_2,y_2)=(4,10)$. For the x - coordinate, $\frac{x_1 + x_2}{2}=\frac{-2 + 4}{2}=\frac{2}{2}=1$.

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

For the y - coordinate, $\frac{y_1 + y_2}{2}=\frac{1+10}{2}=\frac{11}{2}=5.5$.

Answer:

Since using the mid - point formula for the points $(-2,1)$ and $(4,10)$ gives the coordinates $(1,5.5)$, $(1,5.5)$ is the mid - point of the line segment with endpoints $(-2,1)$ and $(4,10)$.