Answer
The points are collinear.
$d(A, B)+d(B, C)=d(A, C)$
$4\sqrt{5}+2\sqrt{5}=6\sqrt{5}$
Work Step by Step
To calculate the distance we will use the distance formula
$A(x_1, y_1)$ $B(x_2, y_2)$
$$d(A, B)=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$$
$d(A, B)=\sqrt{(3-(-1))^2+(11-3)^2}=\sqrt{16+64}=\sqrt{80}=4\sqrt{5}$
$d(B, C)=\sqrt{(5-3)^2+(15-11)^2}=\sqrt{4+16}=\sqrt{20}=2\sqrt{5}$
$d(A, C)=\sqrt{(5-(-1))^2+(15-3)^2}=\sqrt{36+144}=\sqrt{180}=6\sqrt{5}$
$d(A, B)+d(B, C)=d(A, C)$
$4\sqrt{5}+2\sqrt{5}=6\sqrt{5}$
So, these points are collinear.
