Answer: The length of segment [tex]\overline{ST}[/tex] is [tex]4\sqrt{2}[/tex] in radical form. I'm unable to see how far to round to, so the decimal form is [tex]5.65685...[/tex]. You will have to round to what the problem asks. The midpoint of the segment is [tex](1,0 )[/tex].
Step-by-step explanation:
To find the length of a line segment, use the distance formula [tex]d=\sqrt{(x_{2}-x_{1} )^{2}+(y_{2}-y_{1})^{2}}[/tex] and solve.
[tex]d=\sqrt{(3-(-1) )^{2}+(-2-2)^{2}}[/tex]
[tex]d=\sqrt{(4)^{2}+(-4)^{2}}=\sqrt{16+16} =\sqrt{32} =\sqrt{2^{5}} =\sqrt{2^{4}\times2} =\sqrt{2^{4}}\times\sqrt{2} =4\sqrt{2}[/tex]
To find the midpoint of a line segment, use the formula [tex]M(\frac{x_{1}+x_{2}}{2} ,\frac{y_{1}+y_{2}}{2} )[/tex] and solve.
[tex]M(\frac{-1+3}{2} ,\frac{2+(-2)}{2} )[/tex]
[tex]M(1,0)[/tex]
