Answer:
see explanation
Step-by-step explanation:
To show the points are collinear, that is lie on the same line.
Then the slope between A and B, B and C must be equal
Calculate slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = A(- 3, - 1) and (x₂, y₂ ) = B(6, 5)
[tex]m_{AB}[/tex] = [tex]\frac{5+1}{6+3}[/tex] = [tex]\frac{6}{9}[/tex] = [tex]\frac{2}{3}[/tex]
Repeat with (x₁, y₁ ) = B(6, 5) and (x₂, y₂ ) = C(3, 3)
[tex]m_{BC}[/tex] = [tex]\frac{3-5}{3-6}[/tex] = [tex]\frac{-2}{-3}[/tex] = [tex]\frac{2}{3}[/tex]
Since the slope between the 2 segments are equal and there is a common point B.
Then the points A, B and C are collinear
