Question

You can use the coordinates of the vertices of triangles and the distance formula to classify triangles cording to their sides. Write the name of cach triangle with the discovered information of their side 1. Find the lengths of each side using the distance formula. For all problems below: Leave answers exact in square root form. A(5,8), B(-3,6), C(0,-5)

Answer 1

the given points are,

A(5,8), B(-3,6), C(0,-5)​

the distance AB is,

`AB=\sqrt[]{(5-\mleft(-3\mright))^2+(8-6)^2}`
`\begin{gathered} AB=\sqrt[]{8^2+2^(^2)} \\ AB=\sqrt[]{64+4} \\ AB=\sqrt[]{68} \end{gathered}`

so, AB = root 68

distance BC is,

`BC=\sqrt[]{(-3-0)^2+(6-(-5))^2}`
`\begin{gathered} AB=\sqrt[]{9+11^2} \\ AB=\sqrt[]{9+121} \\ AB=\sqrt[]{130} \end{gathered}`

the distance CA

`CA=\sqrt[]{(0-5)^2+(-5-8)^2}`
`\begin{gathered} CA=\sqrt[]{5^2+(-13)^2} \\ CA=\sqrt[]{25+169} \\ CA=\sqrt[]{194} \end{gathered}`