About Collinear Points Distance Formula Method:

In some cases, we need to determine if three points are collinear, which means they lie on the same line. There are many methods that can be used for this procedure. Here we will use a method that relies on our distance formula. Essentially, if three points are collinear, then the sum of the distances between two pairs of points will be equal to the distance between the remaining pair of points. We can use our distance formula to find the three distances involved and then check to see if the two smaller distances sum to the largest distance.

Test Objectives
  • Demonstrate an understanding of the Pythagorean Formula
  • Demonstrate an understanding of the distance formula
  • Demonstrate the ability to determine if three points are collinear
Collinear Points Distance Formula Method Practice Test:

#1:

Instructions: determine whether the points are collinear.

$$a)\hspace{.2em}(-1,-2), (1,8), (-2,-7)$$

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#2:

Instructions: determine whether the points are collinear.

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

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#3:

Instructions: determine whether the points are collinear.

$$a)\hspace{.2em}(4,0), (-1,5), (8,-4)$$

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#4:

Instructions: determine whether the points are collinear.

$$a)\hspace{.2em}(-2,-1), (-3,-3), \left(\frac{3}{2},6\right)$$

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#5:

Instructions: determine whether the points are collinear.

$$a)\hspace{.2em}(-5,-5), (-2,0), (0,2)$$

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Written Solutions:

#1:

Solutions:

$$a)\hspace{.2em}\text{Collinear}$$ Graphing (-1, -2), (1, 8), and (-2, -7)

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#2:

Solutions:

$$a)\hspace{.2em}\text{Not Collinear}$$ Graphing (3, 1), (-2, -1), and (-8, 8)

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#3:

Solutions:

$$a)\hspace{.2em}\text{Collinear}$$ Graphing (4, 0), (-1, 5), and (8, -4)

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#4:

Solutions:

$$a)\hspace{.2em}\text{Collinear}$$ Graphing (-2, -1), (-3, -3), and (3/2, 6)

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#5:

Solutions:

$$a)\hspace{.2em}\text{Not Collinear}$$ Graphing (-5, -5), (-2, 0), and (0, 2)

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