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9-12 Integrated Math 2 Unit 7 Lesson 1

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K-5 Math 6-8 Math •9-12 Math

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Integrated Math 1 •Integrated Math 2 Integrated Math 3

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Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 •Unit 7 Unit 8

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Unit 7, Lesson 1

Connecting Distance and Circles

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Integrated Math 2

Practice

Problem 1

Find the distance between these points: \((\text-2,\text-3)\) and \((4,7)\).

Problem 2

Plot as many points as you can that lie a distance of 5 away from the point \((\text-2,\text-3)\).

Problem 3

For each point, determine whether it lies on a circle centered at \((5,\text-6)\) with a radius of \(\sqrt{10}\). Explain how you know.

\((6,\text-3)\)
\((2,\text-6)\)

Problem 4

A circle has a center at \((2,2)\). What is the radius of the circle if:

\((\text-1,4)\) lies on the circle?
\((3,7)\) lies on the circle?

Problem 5

Find the distance between these points: \((\text-3,1)\) and \((4,\text-6)\).

Problem 6

Plot as many points as you can that lie a distance of 5 away from the point \((1,4)\).

Problem 7

For each point, determine whether it lies on a circle centered at \((\text-7,7)\) with a radius of \(\sqrt{13}\). Explain how you know.

\((\text-5,4)\)
\((\text-4,7)\)

Problem 8

A circle has a center at \((3,4)\). What is the radius of the circle if:

\((\text-2, \text-1)\) lies on the circle?
\((4, \text-5)\) lies on the circle?