Question

What is the midpoint and distance of ( -6 , 5), (-1 , -2)

Answer 1

The midpoint of given points is $\left(\frac{-7}{2}, \frac{3}{2}\right)$

The distance between the given points is 8.6023 units

Solution:

Given that two points are (-6, 5) and (-1, -2)

We have to find the midpoint and distance

The midpoint of two given points is given as:

$m(x, y)=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)$

Here in this sum,

$x_{1}=-6 ; x_{2}=-1 ; y_{1}=5 ; y_{2}=-2$

Substituting the values in formula, we get

$\begin{aligned}&m(x, y)=\left(\frac{-6+(-1)}{2}, \frac{5+(-2)}{2}\right)\\\\&m(x, y)=\left(\frac{-7}{2}, \frac{3}{2}\right)\end{aligned}$

Thus the midpoint of given points is $\left(\frac{-7}{2}, \frac{3}{2}\right)$

Distance between given points:

The formula for distance is given as:

$D=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}$

Substituting the values in formula, we get

$\begin{aligned}&D=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}\\\\&D=\sqrt{(-1-(-6))^{2}+(-2-5)^{2}}\\\\&D=\sqrt{5^{2}+(-2-5)^{2}}\\\\&D=\sqrt{25+49}=\sqrt{74}\end{aligned}$

D = 8.6023 units

Thus the distance between the given points is 8.6023 units