### 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) $$(3,-5),(-7,3)$$

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#2:

Instructions: Find the distance between each pair of points.

a) $$(4,-6),(-12,10)$$

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#3:

Instructions: Find the distance between each pair of points.

a) $$(8,-1),(11,-2)$$

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#4:

Instructions: Find the distance between each pair of points.

a) $$(5,0),(-10,10)$$

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#5:

Instructions: Find the distance between each pair of points.

a) $$(1,2),(-7,-10)$$

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Written Solutions:

#1:

Solutions:

a) $$d = 2\sqrt{41}$$

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#2:

Solutions:

a) $$d = 16\sqrt{2}$$

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#3:

Solutions:

a) $$d = \sqrt{10}$$

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#4:

Solutions:

a) $$d = 5\sqrt{13}$$

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#5:

Solutions:

a) $$d = 4\sqrt{13}$$