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
#1:
Instructions: determine if collinear.
$$a)\hspace{.2em}(2,7), (1,2), (0,-3)$$
$$b)\hspace{.2em}(5,-1), (9,0), (0,-4)$$
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#2:
Instructions: determine if collinear.
$$a)\hspace{.2em}(-3,-5), (6,2), (7,1)$$
$$b)\hspace{.2em}\left(\frac{7}{2},0\right), (2,3), (5,-3)$$
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#3:
Instructions: determine if collinear.
$$a)\hspace{.2em}(1,8), (2,-1), (3,-10)$$
$$b)\hspace{.2em}(4,-1), (3,-7), (10,5)$$
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#4:
Instructions: determine if collinear.
$$a)\hspace{.2em}(8,-13), (3,-2), (0,-1)$$
$$b)\hspace{.2em}(0,-8), (9,0), (-4,13)$$
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#5:
Instructions: determine if collinear.
$$a)\hspace{.2em}(1,-1), (2,-5), (3,-9)$$
$$b)\hspace{.2em}(0,5), (1,-7), (2,-19)$$
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Written Solutions:
#1:
Solutions:
$$a)\hspace{.2em}Collinear$$
$$b)\hspace{.2em}Not \hspace{.2em}Collinear$$
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#2:
Solutions:
$$a)\hspace{.2em}Not \hspace{.2em}Collinear$$
$$b)\hspace{.2em}Collinear$$
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#3:
Solutions:
$$a)\hspace{.2em}Collinear$$
$$b)\hspace{.2em}Not \hspace{.2em}Collinear$$
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#4:
Solutions:
$$a)\hspace{.2em}Not \hspace{.2em}Collinear$$
$$b)\hspace{.2em}Not \hspace{.2em}Collinear$$
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#5:
Solutions:
$$a)\hspace{.2em}Collinear$$
$$b)\hspace{.2em}Collinear$$
