Question

Find the length of the segment. Then find the coordinates of the midpoint of the segment.

Answer 1

Answer: The length of segment
`\overline{ST}` is
`4√(2)` in radical form. I'm unable to see how far to round to, so the decimal form is
`5.65685...`. You will have to round to what the problem asks. The midpoint of the segment is
`(1,0 )`.

Explanation:

To find the length of a line segment, use the distance formula
`d=\sqrt{(x_(2)-x_(1) )^(2)+(y_(2)-y_(1))^(2)}` and solve.

`d=\sqrt{(3-(-1) )^(2)+(-2-2)^(2)}`

`d=\sqrt{(4)^(2)+(-4)^(2)}=√(16+16) =√(32) =\sqrt{2^(5)} =\sqrt{2^(4)*2} =\sqrt{2^(4)}*√(2) =4√(2)`

To find the midpoint of a line segment, use the formula
`M((x_(1)+x_(2))/(2) ,(y_(1)+y_(2))/(2) )` and solve.

`M((-1+3)/(2) ,(2+(-2))/(2) )`

`M(1,0)`