Question

please find the slopes and lengths then fill in the words that best describes the type of quadrilateral.

Answer 1

We can find the slopes using the following formula:

`m=(y2-y1)/(x2-x1)`

And the lengths using the following formulas:

`d=\sqrt[]{(x2-x1)^2+(y2-y1)^2}`

Therefore:

`m_(QR)=(5-2)/(-1-(-9))=(3)/(8)`
`m_(RS)=(9-5)/(1-(-1))=(4)/(2)=2`
`m_(ST)=(6-3)/(-7-1)=(3)/(8)`
`m_(TQ)=(6-2)/(-7-(-9))=(4)/(2)=2`
`\begin{gathered} L_(QR)=\sqrt[]{(-1-(-9))^2+(5-2)^2} \\ L_(QR)=\sqrt[]{73} \end{gathered}`
`\begin{gathered} L_(RS)=\sqrt[]{(1-(-1))^2+(9-5)^2} \\ L_(RS)=2\sqrt[]{5} \end{gathered}`
`\begin{gathered} L_(ST)=\sqrt[]{(6-9)^2+(-7-1)^2} \\ L_(ST)=\sqrt[]{73} \end{gathered}`
`\begin{gathered} L_(TQ)=\sqrt[]{(6-2)^2+(-7-(-9))^2}_{} \\ L_(TQ)=2\sqrt[]{5} \end{gathered}`

Since:

`\begin{gathered} m_(RS)=m_(TQ)\to m_(RS)\parallel m_(TQ) \\ m_(QR)=m_(ST)\to m_(QR)\parallel m_(ST) \end{gathered}`

And:

`\begin{gathered} L_(QR)=L_(ST) \\ L_(RS)=L_(QT) \end{gathered}`

According to this, we can conclude it is a parallelogram