Q 33. - Precalculus Enhanced with Graphing Utilities

Question

Show that the points $A\left(2,5\right) , B\left(6,1\right)$ and

$C\left(8,-1\right)$ lie on a straight line by using slopes.

Step-by-Step Solution

Answer

Since all three slopes $m_{1 ,}{m}_2 ,m_3$ are same so they are lie on a straight line.

Step 1. Given information.

Consider the given information such that the points $A\left(2,5\right) ,B\left(6,1\right)$ and $C\left(8,-1\right)$.

Step 2. Using the slope formula . m = y 2 - y 1 x 2 - x 1

Formula used to calculate slope between $A$and $B$ ,$B$ and $C$ ,$C$ and $A$.

$$\begin{gathered} m_{AB}=\frac{1-5}{6-2} \\ {m}_{AB}=-1 \end{gathered}$$

Similarly,$m_{BC}=-1$ and $m_{CA}=-1$.