Question

plot the three points on the given coordinate plane. state whether the three points you plotted are collinear (on the same line). (1,2),(-2,3),(4,1)

Explanation:

Step1: Recall slope - formula

The slope formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Calculate slope between $(1,2)$ and $(-2,3)$

Let $(x_1,y_1)=(1,2)$ and $(x_2,y_2)=(-2,3)$. Then $m_1=\frac{3 - 2}{-2 - 1}=\frac{1}{-3}=-\frac{1}{3}$.

Step3: Calculate slope between $(-2,3)$ and $(4,1)$

Let $(x_1,y_1)=(-2,3)$ and $(x_2,y_2)=(4,1)$. Then $m_2=\frac{1 - 3}{4+2}=\frac{-2}{6}=-\frac{1}{3}$.

Step4: Calculate slope between $(1,2)$ and $(4,1)$

Let $(x_1,y_1)=(1,2)$ and $(x_2,y_2)=(4,1)$. Then $m_3=\frac{1 - 2}{4 - 1}=\frac{-1}{3}=-\frac{1}{3}$.

Step5: Determine collinearity

Since $m_1 = m_2=m_3=-\frac{1}{3}$, the three points $(1,2),(-2,3),(4,1)$ are collinear.

Answer:

The three points $(1,2),(-2,3),(4,1)$ are collinear.