Question

Say true or false:

Points $P(10,-6),Q(6,-4)$ and $C(-8,3)$ are collinear.

• A. True
• B. False

Answer 1

The correct option is A True

Since the slope of the line with points $(x_1,y_1)$ and $(x_2,y_2)$ is:

$m=\frac{y_2-y_1}{x_2-x_1}$

We find the slope of the line $PQ$ with points $P(10,-6)$ and $Q(6,-4)$ is:

$m=\frac{-4-(-6)}{6-10}=\frac{-4+6}{-4}=-\frac{1}{2}$

Now the slope of the line $QC$ with points $Q(6,-4)$ and $C(-8,3)$ is:

$m=\frac{3-(-4)}{-8-6}=\frac{7}{-14}=-\frac{1}{2}$

Finally the slope of the line $PC$ with points $P(10,-6)$ and $C(-8,3)$ is:

$m=\frac{3-(-6)}{-8-10}=\frac{9}{-18}=-\frac{1}{2}$

Since the slope of $PQ$, $QC$ and $PC$ are equal, therefore, the points are collinear.