Question

Show exact steps o solve! Solve using the distance formula!Answer #3

Answer 1

Given:

The triangle SUE is,

a) To prove the given triangle is right triagle,

Find the distance between each point and then use pythagoean thoerem to show the given traingle is right triangle.

`\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2^{}} \\ d(SE)=\sqrt[]{(8-(-2))^2+(-9-(-4))^2} \\ =\sqrt[]{10^2+(-5)^2} \\ =\sqrt[]{125} \\ =5\sqrt[]{5} \end{gathered}`
`\begin{gathered} d(SU)=\sqrt[]{(2-(-2))^2+(-1-(-4))^2} \\ =\sqrt[]{4^2+3^2} \\ =\sqrt[]{25} \\ =5 \end{gathered}`

`\begin{gathered} d(UE)=\sqrt[]{(8-2)^2+(-9-(-1))^2} \\ =\sqrt[]{6^2+(-8)^2} \\ =\sqrt[]{100} \\ =10 \end{gathered}`

So, the length of the sides of the triangle is,

`\begin{gathered} SE=5\sqrt[]{5} \\ SU=5 \\ UE=10 \end{gathered}`

It is obsereved that,

`\begin{gathered} (SU)^2+(UE)^2=5^2+10^2 \\ =25+100 \\ =125 \\ (SE)^2=(5\sqrt[]{5})^2=25*5=125 \\ \Rightarrow(SE)^2=(SU)^2+(UE)^2 \end{gathered}`

Thus, the longer side is equivalent to other two sides.

Hence, the given triangle SUE is right triangle.

b) Isosceles triangle: the triangle that has two sides of equal length.

But in the given triangle does not have two equal sides.

So, the given traingle is not Isosceles rigth triangle.