Answer:
see explanation
Step-by-step explanation:
Calculate the slopes between pairs of the 3 points using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 9, 3) and (x₂, y₂ ) = (- 3, 9)
m = [tex]\frac{9-3}{-3-(-9)}[/tex] = [tex]\frac{6}{-3+9}[/tex] = [tex]\frac{6}{6}[/tex] = 1
Repeat with (x₁, y₁ ) = (5, 1) and (x₂, y₂ ) = (- 3, 9)
m = [tex]\frac{9-1}{-3-5}[/tex] = [tex]\frac{8}{-8}[/tex] = - 1
If lines are perpendicular then the product of their slopes = - 1 , then
1 × - 1 = -1
Thus there is a right angle between the 2 lines
Then triangle is right- angled
