Answer:
the triangle ABC of the figure is an isosceles triangle
Step-by-step explanation:
we have
[tex]A(8,2),B(11,13),C(2,6)[/tex]
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 [tex]AB=BC[/tex]
Remember that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
Find the distance AB
we have
[tex]A(8,2),B(11,13)[/tex]
substitute in the formula
[tex]d=\sqrt{(13-2)^{2}+(11-8)^{2}}[/tex]
[tex]d=\sqrt{(11)^{2}+(3)^{2}}[/tex]
[tex]dAB=\sqrt{130}\ units[/tex]
Find the distance BC
we have
[tex]B(11,13),C(2,6)[/tex]
substitute in the formula
[tex]d=\sqrt{(6-13)^{2}+(2-11)^{2}}[/tex]
[tex]d=\sqrt{(-7)^{2}+(-9)^{2}}[/tex]
[tex]dBC=\sqrt{130}\ units[/tex]
therefore
[tex]AB=BC[/tex] -------> the triangle ABC of the figure is an isosceles triangle
