Respuesta :
A perpendicular bisector is a line that divides a segment into 2 equal portions and forms a right angle while doing it.
According to the prependicular bisector theorem, a point lies on the perpendicular line of a segment if the point has the same distance from the ending points of the segment.
The distance can be calculated with the formula
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]8.
Calculate the distance between points S and R
S=(4,-2)
R=(3,7)
[tex]\begin{gathered} d=\sqrt[]{(3-4)^2+(7-(-2))^2} \\ d=\sqrt[]{(-1)^2+(9)^2} \\ d=\sqrt[]{82} \end{gathered}[/tex]calculate the distance between points S and Q
Q=(-5,-1)
S=(4,-2)
[tex]\begin{gathered} d=\sqrt[]{(4-(-5))^2+(-2-(-1)})^2 \\ d=\sqrt[]{(9)^2+(-1)^2} \\ d=\sqrt[]{82} \end{gathered}[/tex]According to the perpendicular bisector theorem, since the distance between the two ends of the segment and the point S are the same, then point S lies on the perpendicular bisector of QR.
9.
Calculate the distance between Q and S
Q=(-5,4)
S=(-2,-5)
[tex]\begin{gathered} d=\sqrt[]{(-2-(-5))^2+(5-4)^2} \\ d=\sqrt[]{(3)^2+(1)^2} \\ d=\sqrt[]{10} \end{gathered}[/tex]