### About Finding the Distance Between Two Points:

We can find the distance between any two points on the coordinate plane by sketching out a right triangle and using the Pythagorean formula. From this formula, we are able to create a distance formula. This distance formula allows us to quickly find the distance between any two points. We simply label the points, plug in, and simplify.

Test Objectives

- Demonstrate a general understanding of the distance formula
- Demonstrate the ability to calculate a square root
- Demonstrate the ability to simplify a square root

#1:

Instructions: find the distance between each pair of points.

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

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#2:

Instructions: find the distance between each pair of points.

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

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#3:

Instructions: find the distance between each pair of points.

$$a)\hspace{.2em}(-9,11),(4,4)$$

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#4:

Instructions: find the distance between each pair of points.

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

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#5:

Instructions: find the distance between each pair of points.

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

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Written Solutions:

#1:

Solutions:

$$a)\hspace{.2em}13$$

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#2:

Solutions:

$$a)\hspace{.2em}3 \sqrt{13}$$

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#3:

Solutions:

$$a)\hspace{.2em}\sqrt{218}$$

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#4:

Solutions:

$$a)\hspace{.2em}10$$

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#5:

Solutions:

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