About Distance Formula:
The Pythagorean Theorem describes the relationship between the lengths of the legs and the hypotenuse in a right triangle. By applying this theorem, we can derive the distance formula, which allows us to calculate the distance between any two points on the Cartesian Coordinate Plane.
Note: For the generate new test option, you will need to be able to simplify a square root, which is covered in the next lesson. Fortunately, it's a very quick process to learn. You can always skip this for now and come back if you are having trouble. The original practice test does not require you to simplify a square root.
Test Objectives
- Demonstrate an understanding of the Pythagorean Theorem
- Demonstrate the ability to set up the distance formula
- Demonstrate the ability to find the distance between two points
#1:
Instructions: Find the distance between each pair of points.
a) $$(-2,1),(-6,1)$$
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#2:
Instructions: Find the distance between each pair of points.
a) $$(3,5),(4,-3)$$
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#3:
Instructions: Find the distance between each pair of points.
a) $$(6,-8),(6,8)$$
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#4:
Instructions: Find the distance between each pair of points.
a) $$(8,-4),(6,-7)$$
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#5:
Instructions: Find the distance between each pair of points.
a) $$(2,-3),(-3,1)$$
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Written Solutions:
#1:
Solutions:
a) $$4$$
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#2:
Solutions:
a) $$\sqrt{65}$$
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#3:
Solutions:
a) $$16$$
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#4:
Solutions:
a) $$\sqrt{13}$$
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#5:
Solutions:
a) $$\sqrt{41}$$