Question

Quadrilateral KAT E has vertices K (1,5), A(4,7), T (7,3), and B(1, -1). Prove that quadrilateral K ATD is a trapezoid,

Answer 1

$\begin{gathered} \text{Let's use the distance formula:} \\ d=\sqrt[]{(x2-x1)^2+(y2-y1)^2} \\ ------ \\ mKA=\sqrt[]{(4-1)^2+(7-5)^2}=\sqrt[]{13} \\ mAT=\sqrt[]{(7-4)^2+(3-7)^2}=\sqrt[]{25}=5 \end{gathered}$$\begin{gathered} mTE=\sqrt[]{(1-7)^2+(-1-3)^2}=\sqrt[]{52}=2\sqrt[]{13} \\ mKE=\sqrt[]{(1-1)^2+(-1-5)}=\sqrt[]{36}=6 \end{gathered}$