### About Collinear Points Using Determinants:

In some cases, we may be asked to determine if three points are collinear using determinants. In the last lesson, we looked at how we could find the area of a triangle using determinants. Here, we will rely on the same formula and look for a specific result. Basically, if this formula evaluates to zero, this tells us the three points are collinear or lie on the same line.

Test Objectives
• Demonstrate the ability to find the determinant of a matrix
• Demonstrate the ability to determine if three points are collinear
Collinear Points Using Determinants Practice Test:

#1:

Instructions: determine if collinear.

$$a)\hspace{.2em}(2,7), (1,2), (0,-3)$$

$$b)\hspace{.2em}(5,-1), (9,0), (0,-4)$$

#2:

Instructions: determine if collinear.

$$a)\hspace{.2em}(-3,-5), (6,2), (7,1)$$

$$b)\hspace{.2em}\left(\frac{7}{2},0\right), (2,3), (5,-3)$$

#3:

Instructions: determine if collinear.

$$a)\hspace{.2em}(1,8), (2,-1), (3,-10)$$

$$b)\hspace{.2em}(4,-1), (3,-7), (10,5)$$

#4:

Instructions: determine if collinear.

$$a)\hspace{.2em}(8,-13), (3,-2), (0,-1)$$

$$b)\hspace{.2em}(0,-8), (9,0), (-4,13)$$

#5:

Instructions: determine if collinear.

$$a)\hspace{.2em}(1,-1), (2,-5), (3,-9)$$

$$b)\hspace{.2em}(0,5), (1,-7), (2,-19)$$

Written Solutions:

#1:

Solutions:

$$a)\hspace{.2em}Collinear$$

$$b)\hspace{.2em}Not \hspace{.2em}Collinear$$

#2:

Solutions:

$$a)\hspace{.2em}Not \hspace{.2em}Collinear$$

$$b)\hspace{.2em}Collinear$$

#3:

Solutions:

$$a)\hspace{.2em}Collinear$$

$$b)\hspace{.2em}Not \hspace{.2em}Collinear$$

#4:

Solutions:

$$a)\hspace{.2em}Not \hspace{.2em}Collinear$$

$$b)\hspace{.2em}Not \hspace{.2em}Collinear$$

#5:

Solutions:

$$a)\hspace{.2em}Collinear$$

$$b)\hspace{.2em}Collinear$$