Question

If A = (8, 2) B = (11, 13) and C = (2, 6), classify the the following triangle as either right or isosceles

Answer 1

The following triangle is isosceles.

Answer 2

Answer:

the triangle ABC of the figure is an isosceles triangle

Step-by-step explanation:

we have

$A(8,2),B(11,13),C(2,6)$        

Using a graphing tool

Plot the triangle

see the attached figure

The triangle in the figure is not a right triangle ------> Is an acute triangle

Verify if the triangle ABC is an isosceles triangle

we know that

An isosceles triangle has two equal sides and two equal angles

Verify if $AB=BC$

Remember that

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

Find the distance AB

we have

$A(8,2),B(11,13)$    

substitute in the formula

$d=\sqrt{(13-2)^{2}+(11-8)^{2}}$

$d=\sqrt{(11)^{2}+(3)^{2}}$

$dAB=\sqrt{130}\ units$

Find the distance BC

we have

$B(11,13),C(2,6)$      

substitute in the formula

$d=\sqrt{(6-13)^{2}+(2-11)^{2}}$

$d=\sqrt{(-7)^{2}+(-9)^{2}}$

$dBC=\sqrt{130}\ units$

therefore

$AB=BC$ -------> the triangle ABC of the figure is an isosceles triangle