Question

For questions 8 and 9, determine if S could lie on the perpendicular bisector of QR with thegiven coordinates.8. Q(-5, -1), R(3, 7), S(4,-2)9. Q(-5, 4), R(8.-3), S(-2.-5)How do you solve this problem?

Answer 1

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

`d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}`

8.

Calculate the distance between points S and R

S=(4,-2)

R=(3,7)

`\begin{gathered} d=\sqrt[]{(3-4)^2+(7-(-2))^2} \\ d=\sqrt[]{(-1)^2+(9)^2} \\ d=\sqrt[]{82} \end{gathered}`

calculate the distance between points S and Q

Q=(-5,-1)

S=(4,-2)

`\begin{gathered} d=\sqrt[]{(4-(-5))^2+(-2-(-1)})^2 \\ d=\sqrt[]{(9)^2+(-1)^2} \\ d=\sqrt[]{82} \end{gathered}`

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)

`\begin{gathered} d=\sqrt[]{(-2-(-5))^2+(5-4)^2} \\ d=\sqrt[]{(3)^2+(1)^2} \\ d=\sqrt[]{10} \end{gathered}`