Question

Find the length and midpoint of the segment with the given endpoints
(-7,-10,9), (-2,9,-9)

Answer 1

26.65, (–4.5, –0.5, 0)

Explanation:

Answer 2

`\large\boxed{d=√(710)\approx26.65}\\\boxed{M(-4.5,\ -0.5,\ 0)}`

Explanation:

`\text{The formula of a length of the sebment:}\\\\d=√((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2)\\\\\text{The formula of a midpoint:}\\\\M\left((x_1+x_2)/(2),\ (y_1+y_2)/(2);\ (z_1+z_2)/(2)\right)`

`\text{We have the endpoints of the segment:}\ (-7,\ -10,\ 9)\ \text{and}\ (-2,\ 9,\ -9).\\\\\text{Substitute}\\\\d=√((-2-(-7))^2+(9-(-10))^2+(-9-9)^2)\\\\d=√(5^2+19^2+(-18)^2)\\\\d=√(25+361+324)\\\\d=√(710)\\\\M(x,\ y,\ z)\\\\x=((-7)+(-2))/(2)=(-9)/(2)=-4.5\\\\y=((-10)+9)/(2)=(-1)/(2)=-0.5\\\\z=(9+(-9))/(2)=(0)/(2)=0\\\\M(-4.5,\ -0.5,\ 0)`