Question

Exercise #1: We would like to find the distance between points A and B if they have coordinates A(2,3) and B(14, 12).

Answer 1

This triangle is isosceles if:

$AB=BC$

Using the distance formula:

$\begin{gathered} AB=\sqrt[]{(x2-x1)^2+(y2-y1)^2} \\ (x1,y1)=(-3,8) \\ (x2,y2)=(-9,0) \\ AB=\sqrt[]{(-9-(-3))^2+(0-8)^2} \\ AB=\sqrt[]{60} \\ \end{gathered}$$\begin{gathered} BC=\sqrt[]{(x2-x1)^2+(y2-y1)^2} \\ (x1,y1)=(-9,0) \\ (x2,y2)=(5,2) \\ BC=\sqrt[]{(5-(-9))^2+(2-0)^2} \\ BC=\sqrt[]{200} \end{gathered}$

Since:

$AB\ne BC$

We can conclude that:

$\Delta ABC$

Is not an isosceles triangle