The triangle does not represent aright-angled triangle
The coordinates of the triangle are given as:
[tex]\mathbf{A = (4,4)}[/tex]
[tex]\mathbf{B = (5,6)}[/tex]
[tex]\mathbf{C = (8,2)}[/tex]
Start by calculating the slopes of the lines that pass through the vertices of the triangles using:
[tex]\mathbf{m = \frac{y_2 - y_1}{x_ 2 -x_1}}[/tex]
So, we have:
[tex]\mathbf{m_{AB} = \frac{6- 4}{5 -4}}[/tex]
[tex]\mathbf{m_{AB} = \frac{2}{1}}[/tex]
[tex]\mathbf{m_{AB} = 2}[/tex] --- the slope of line AB
[tex]\mathbf{m_{CB} = \frac{6- 2}{5 -8}}[/tex]
[tex]\mathbf{m_{CB} = \frac{4}{-3}}[/tex]
[tex]\mathbf{m_{CB} = -\frac{4}{3}}[/tex] --- the slope of line CB
[tex]\mathbf{m_{AC} = \frac{4- 2}{4 -8}}[/tex]
[tex]\mathbf{m_{AC} = \frac{- 2}{-4}}[/tex]
[tex]\mathbf{m_{AC} = \frac{1}{2}}[/tex] --- the slope of line AC
None of the slopes have the following relationship with another slope
[tex]\mathbf{m_1 = -\frac{1}{m_2}}[/tex] --- condition for perpendicular line
Hence, the triangle is not a right-angled triangle
Read more about triangles at:
https://brainly.com/question/3189840
