Answer:
Step-by-step explanation:
Find the lenghth of the left and right sides using the distance formula to determine if the trapeziod is isosceles
[tex]d=\sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2}[/tex]
[tex]PS=\sqrt{(2-1)^2+(0-4)^2}[/tex]
[tex]PS=[/tex][tex]\sqrt{17}[/tex]
[tex]QR=\sqrt{(13-9)^{2}+(8-10)^{2}}[/tex]
[tex]QR=[/tex][tex]\sqrt{20}[/tex]
Since [tex]PS\neq QR[/tex] (the sides are not equal) this is not an isosceles trapezoid
Sally is incorrect and John is possibly correct.
Find the slope of the top and bottom sides to determine if this is a trapezoid.
[tex]m=[/tex] [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
SR: [tex]m=[/tex] [tex]\frac{0-8}{2-13}[/tex]
[tex]m=\frac{8}{11}[/tex]
PQ: [tex]m=\frac{4-10}{1-9}[/tex]
[tex]m=\frac{6}{8}=\frac{3}{4}[/tex]
since [tex]mSR\neq mPQ[/tex] (the slopes are not equal) the top and bottom sides are not parallel therefore this is not a trapezoid. Hence, John is incorrect, and Mary is ultimately correct.
