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Using the diagram below, determine what kind of triangle PQR is based on its sides.

Using the diagram below, determine what kind of triangle PQR is based on its sides-example-1
User Sola Oderinde
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1 Answer

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The coordinates of the vertices of triangle are,

P(-4,2), Q(2,-5) and R(5,4).

Determine the length of side PQ by using distance formula.


\begin{gathered} PQ=\sqrt[]{(2-(-4))^2+(-5-2)^2} \\ =\sqrt[]{(6)^2+(7)^2} \\ =\sqrt[]{36+49} \\ =\sqrt[]{85} \end{gathered}

Determine the length of side PR by using distance formula.


\begin{gathered} PR=\sqrt[]{(-4-5)^2+(2-4)^2} \\ =\sqrt[]{(-9)^2+(2)^2} \\ =\sqrt[]{81+4} \\ =\sqrt[]{85} \end{gathered}

Determine the length of side QR by using distance formula.


\begin{gathered} QR=\sqrt[]{(2-5)^2+(-5-4)^2} \\ =\sqrt[]{(3)^2+(-9)^2} \\ =\sqrt[]{9+81} \\ =\sqrt[]{90} \end{gathered}

Since length of side PR and side PQ is equal to each. The triangle with two equal sides are called isosceles triangle.

So triangle PQR is isosceles triangle.

User Scott McKenzie
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