Chapter 9.3, Problem 3ST

  

To determine

To find: The given lines are collinear or not.

Answer to Problem 3ST

The given three lines are not collinear.

Explanation of Solution

Given information: The points are $A\left(2,2\right),B\left(8,6\right)andC\left(11,10\right)$ .

Formula used: Slope of $XY=\frac{y_2-y_1}{x_2-x_1}$

Calculation: Apply the formula to get the slope of the lines,

  $\begin{array}{l}AB=\frac{y_2-y_1}{x_2-x_1}\\ =\frac{6-2}{8-2}\\ =\frac{4}{6}\\ \therefore AB=\frac{2}{3}\end{array}$

Likewise for other two slopes .i.e. BC and AC.

  $\begin{array}{l}BC=\frac{10-6}{11-8}=\frac{4}{3}\\ CA=\frac{11-2}{10-2}=\frac{9}{8}\end{array}$

Here, $AB\ne BC\ne CA$

Since, if the slopes of the lines are not same then the lines are not said to be collinear.

Hence, the given lines are not collinear.