Question

Please helpFind the desired slopes and lengths then fill in the words that characterize the triangle.Options for triangle STU is…Isosceles rightScalene rightIsosceles and not rightScalene and not right

Answer 1

In order to determine the slope of a line, we need two known points (x1, y1) and (x2, y2), then we need to use the following expression:

`m=(y_2-y_1)/(x_2-x_1)`

In order to determine the slopes, we will use the expression above and choose two points that belong to the lines.

The slope of ST:

`\text{mST}=(8-7)/(6-1)=(1)/(5)`

The slope of TU:

`mTU=(-2-8)/(8-6)=(-10)/(2)=-5`

The slope of US:

`\text{mUS}=(-2-7)/(8-1)=(-9)/(7)`

In order to determine the length of a segment, we need to calculate the distance between the two endpoints of that segment. This is done by using the following formula:

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

The length of ST is:

`\begin{gathered} d=\sqrt[]{(8-7)^2+(6-1)^2} \\ d=\sqrt[]{1^2+5^2} \\ d=\sqrt[]{1+25} \\ d=\sqrt[]{26}=5.1 \end{gathered}`

The length of TU is:

`\begin{gathered} d=\sqrt[]{(-2-8)^2+(8-6)^2} \\ d=\sqrt[]{(-10)^2+(2)^2} \\ d=\sqrt[]{100+4} \\ d=\sqrt[]{104}=10.2 \end{gathered}`

The length of US is:

`\begin{gathered} d=\sqrt[]{(-2-7)^2+(8-1)^2} \\ d=\sqrt[]{(-9)^2+(7)^2} \\ d=\sqrt[]{81+49} \\ d=\sqrt[]{130} \\ d=11.4 \end{gathered}`

The triangle STU is scalene right.