Question

plot the three points on the given coordinate plane. (3, 1), (-2, -3), (4, 0)
state whether the three points you plotted appear to be collinear (on the same line). collinear
not collinear

Explanation:

Step1: Recall point - plotting rule

In a coordinate plane, for a point $(x,y)$, $x$ is the horizontal coordinate and $y$ is the vertical coordinate.

Step2: Plot the point $(3,1)$

Move 3 units to the right along the x - axis and 1 unit up along the y - axis and mark the point.

Step3: Plot the point $(-2,-3)$

Move 2 units to the left along the x - axis and 3 units down along the y - axis and mark the point.

Step4: Plot the point $(4,0)$

Move 4 units to the right along the x - axis (since $y = 0$, there is no vertical movement) and mark the point.

Step5: Check collinearity

Calculate the slope between two pairs of points. The slope formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$.
Let $(x_1,y_1)=(3,1)$ and $(x_2,y_2)=(-2,-3)$. Then $m_1=\frac{-3 - 1}{-2 - 3}=\frac{-4}{-5}=\frac{4}{5}$.
Let $(x_1,y_1)=(-2,-3)$ and $(x_2,y_2)=(4,0)$. Then $m_2=\frac{0+3}{4 + 2}=\frac{3}{6}=\frac{1}{2}$.
Since $m_1
eq m_2$, the points are not on the same line.

Answer:

not collinear