Question

find the midpoint of the line segment with the given endpoints. (10,\sqrt{7}) and (-6,3\sqrt{7})

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: Identify the values of $x_1,x_2,y_1,y_2$

Here $x_1 = 10$, $x_2=-6$, $y_1=\sqrt{7}$, $y_2 = 3\sqrt{7}$.

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

$\frac{x_1 + x_2}{2}=\frac{10+( - 6)}{2}=\frac{10 - 6}{2}=\frac{4}{2}=2$.

Step4: Calculate the y - coordinate of the mid - point

$\frac{y_1 + y_2}{2}=\frac{\sqrt{7}+3\sqrt{7}}{2}=\frac{(1 + 3)\sqrt{7}}{2}=\frac{4\sqrt{7}}{2}=2\sqrt{7}$.

Answer:

$(2,2\sqrt{7})$