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