Question

Find the measure of the sides ABC and classify each triangle by its sides A(5, 4) B(3, -1) C (7, -1)

Answer 1

`\begin{gathered} \text{The ordered pairs are given as,} \\ A(5,4),B(3,-1),C(7,-1) \\ \text{The length of the side can be calculated by this expression as follows:} \\ l=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ So,\text{ the length of the side AB is,} \\ l_(AB)=\sqrt[]{(3-5)^2+(-1-4)^2} \\ l_(AB)=\sqrt[]{4+25} \\ l_(AB)=\sqrt[]{29}\text{ unit} \\ So,\text{ the length of the side BC is,} \\ l_(BC)=\sqrt[]{(7-3)^2+(-1+1)^2} \\ l_(BC)=\sqrt[]{4^2+0^2} \\ l_(BC)=4\text{ unit} \\ So,\text{ the length of the side AC is,} \\ l_(AC)=\sqrt[]{(5-7)^2+(4+1)^2} \\ l_(AC)=\sqrt[]{2^2+5^2} \\ l_(AC)=\sqrt[]{29}\text{ unit} \end{gathered}`