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
