Respuesta :
The midpoint of given points is [tex]\left(\frac{-7}{2}, \frac{3}{2}\right)[/tex]
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:
[tex]m(x, y)=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)[/tex]
Here in this sum,
[tex]x_{1}=-6 ; x_{2}=-1 ; y_{1}=5 ; y_{2}=-2[/tex]
Substituting the values in formula, we get
[tex]\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}[/tex]
Thus the midpoint of given points is [tex]\left(\frac{-7}{2}, \frac{3}{2}\right)[/tex]
Distance between given points:
The formula for distance is given as:
[tex]D=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}[/tex]
Substituting the values in formula, we get
[tex]\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}[/tex]
D = 8.6023 units
Thus the distance between the given points is 8.6023 units
