Question

Graph the points and state whether they are collinear.(1,3), (0,2), (-4,0)Use the graphing tool to plot the given points.Click toenlargegraph

Answer 1

the points are not collinear

Explanation

Step 1

Let

A(1,3)

B(0,2)

C(-4,0)

to know if the segments AB and BA are collinear, they must have the same slope if they are

$\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ \text{where} \\ P1(x_1,y_1) \\ P2(x_2,y_2) \\ \end{gathered}$

for segment AB

let

P1=A(1,3)

P2=B(0,2)

$\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ slope_{AB}=\frac{2-3}{0-1}=\frac{-1}{-1}=1 \\ slope_{AB}=1 \end{gathered}$

Step 2

for segment BC

P1=B(0,2)

P2=C(-4,0)

$\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ \text{slope}=\frac{0-2}{-4-0}=\frac{-2}{-4}=\frac{1}{2} \end{gathered}$

Step 3

compare the slopes

$\text{slope}_{AB}\ne slope_{BC}$

then, the points are not collinear