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For three points to be collinear, they must have the same slope.

Step 1. Calculate the slope of the line using the formula $m=\dfrac{y_2-y_1}{x_2-x_1}$

$m=\dfrac{5-1}{-2-0}=-2$

Step 2. From the choices use the guess and check method.

point $(-2,3)$

$-2=\dfrac{5-3}{-2+2}$ the statement is not true

point $(4,5)$

$-2=\dfrac{5-5}{-2-4}$ the statement is not true

point $(2,-3)$

$-2=\dfrac{5+3}{-2-2}$ the statement is true

So the desired answer is $(2,-3)$ .

Basic geometry :) If points are collinear, then all points that share the same equation will sit on the same line.

1) Find the gradient of the line----> $\frac{1-5}{0-(-2)}$ = -2

2) Using our gradient m= -2, input it in the form y=-2x+c

3) Imput any point of your desire. In this case, I will use (0,1).

4) 1= -2(0)+c, 1=c. This means our y intercept is 1.

5) Complete the formula of y= -2x+1

6) Imput the available multiple choice options into your formula. The correct answe is B, or (2,-3)

This means (2,-3) (0,1) and (-2,5) are all collinear. When graphed, they are all on the same line. :)

Learn How to Calculate Collinearity of Three Points - Tutorial