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9-12 Geometry Unit 6 Lesson 2

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K-5 Math 6-8 Math •9-12 Math

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Algebra 1 •Geometry Algebra 2 Extra Support Materials for Algebra 1

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

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Lesson 1 •Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14 Lesson 15 Lesson 16 Lesson 17 Lesson 18

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Algebra 2
Extra Support Materials for Algebra 1

Integrated Math 1
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Lesson 4
Lesson 5
Lesson 6
Lesson 7
Lesson 8
Lesson 9
Lesson 10
Lesson 11
Lesson 12
Lesson 13
Lesson 14
Lesson 15
Lesson 16
Lesson 17
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Unit 6, Lesson 2

Transformations as Functions

Geometry

Practice

Problem 1

Match each coordinate rule to a description of its resulting transformation.

\((x,y) \rightarrow (x+3,y)\)
\((x,y) \rightarrow (2x,2y)\)
\((x,y) \rightarrow (x,y+4)\)
\((x,y) \rightarrow (x,y-4)\)
\((x,y) \rightarrow (x-3,y+4)\)

Translate by the directed line segment from \((0,0)\) to \((0,4)\).
Translate by the directed line segment from \((0,0)\) to \((3,0)\).
Dilate using the origin as the center and a scale factor of 2.
Translate by the directed line segment from \((0,0)\) to \((0,\text-4)\).
Translate by the directed line segment from \((0,0)\) to \((\text-3,4)\).

Problem 2

Draw the image of triangle \(ABC\) under the transformation \((x,y) \rightarrow (x-4,y+1)\). Label the result \(T\).
Draw the image of triangle \(ABC\) under the transformation \((x,y) \rightarrow (\text- x,y)\). Label the result \(R\).

<p>Triangle ABC. A at 2 comma 3, B at 4 comma 2, C at 3 comma 5.</p>

Problem 3

Here are some transformation rules. For each rule, describe whether the transformation is a rigid motion, a dilation, or neither.

\((x,y) \rightarrow (x-2,y-3)\)
\((x,y) \rightarrow (2x,3y)\)
\((x,y) \rightarrow (3x,3y)\)
\((x,y) \rightarrow (2-x,y)\)

Problem 4

ForLesson 1: Rigid Transformations in a Plane

Reflect triangle \(ABC\) over the line \(x=0\). Call this new triangle \(A’B’C’\). Then reflect triangle \(A’B’C’\) over the line \(y=0\). Call the resulting triangle \(A''B''C''\).

Which single transformation takes \(ABC\) to \(A''B''C''\)?

<p>Triangle ABC graphed on coordinate plane. A at 1 comma 1, B at 2 comma -1, C at 3 comma 0.</p>

Translate triangle \(ABC\) by the directed line segment from \((1,1)\) to \((\text-2,1)\).
Reflect triangle \(ABC\) across the line \(y=\text-x\).
Rotate triangle \(ABC\) counterclockwise using the origin as the center by 180 degrees.
Dilate triangle \(ABC\) using the origin as the center and a scale factor of 2.

Problem 5

ForLesson 1: Rigid Transformations in a Plane

Reflect triangle \(ABC\) over the line \(y=2\).

Translate the image by the directed line segment from \((0,0)\) to \((3,2)\).

What are the coordinates of the vertices in the final image?

<p>triangle ABC graphed. A = -5 comma 2, B = -6 comma -1, C = -3 comma 0.</p>

Problem 6

ForLesson 17: Volume and Density

The density of water is 1 gram per cm³. An object floats in water if its density is less than water’s density, and it sinks if its density is greater than water’s. Will a cylindrical log with radius 0.4 meters, height 5 meters, and mass 1,950 kilograms sink or float? Explain your reasoning.

Problem 7

ForLesson 12: Prisms and Pyramids

These 3 congruent square pyramids can be assembled into a cube with side length 3 feet. What is the volume of each pyramid?

<p>Rectangular pyramid </p>

<p>Rectangular pyramid </p>

<p>Rectangular pyramid </p>

1 cubic foot
3 cubic feet
9 cubic feet
27 cubic feet

Problem 8

ForLesson 1: Congruent Parts, Part 1

Reflect square \(ABCD\) across line \(CD\). What is the ratio of the length of segment \(AA'\) to the length of segment \(AD\)? Explain or show your reasoning.

<p>Square ABCD.</p>