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

the triangle ABC of the figure is an isosceles triangle

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=√(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=√(130)\ units`

therefore

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