Lesson 2

Scale of the Solar System

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Problem 1

Figure \(G’\) is the image of figure \(G\) by a dilation with scale factor 2. Where is the center of this dilation?

Points A, B, C, D, figure G, and dilated figure G prime. Figure G looks like an angle whose endpoints are connected by a half-circle, and the vertex of the angle is point C.
A:

Point \(A\)

B:

Point \(B\)

C:

Point \(C\)

D:

Point \(D\)

Solution

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Problem 2

Dilate quadrilateral \(ABCD\) using center \(A\) and scale factor \(\frac{1}{2}\).

Quadrilateral A B C D on isometric grid. Side A B is 2 diagonal units long, side B C is 2 diagonal units long, and side C D is 3 diagonal units long.

Solution

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Problem 3

Triangle \(ABC\) is dilated. The image is \(A'B'C'\), find the value of \(x\). 

Right Triangle A B C. Side A C labeled 6. Side C B labeled 3.  
Right Triangle A prime B prime C prime. Side A prime C prime labeled 4. Side C prime B prime labeled x.  

Solution

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Problem 4

Polygon \(Q\) is a scaled copy of Polygon \(P\).

Polygon P with top side of 4 and right side of x. Polygon Q with top side of 3 and right side of y.

The value of \(x\) is 6, what is the value of \(y\)?

A:

\(\frac72\)

B:

4

C:

\(\frac92\)

D:

5

Solution

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(From Unit 3, Lesson 1.)

Problem 5

Solve each equation.

  1. \(\frac{2}{5}=\frac{x}{20}\)
  2. \(\frac{2}{3}=\frac{x}{10}\)

Solution

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(From Unit 3, Lesson 1.)

Problem 6

\(WXYZ\) is a kite. Angle \(WXY\) has a measure of 94 degrees and angle \(ZYX\) has a measure of 60 degrees. Find the measure of angle \(ZWY\).

Kite W X Y Z. Diagonal W Y is drawn in. Sides Z W and W X have single tick marks. Sides X Y and Y Z have double tick marks.

Solution

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(From Unit 2, Lesson 9.)

Problem 7

The semaphore alphabet is a way to use flags to signal messages. Here's how to signal the letter U. Describe a transformation that would take the right hand flag to the left hand flag.

U

Stick figure with arms up and hand flags labeled R and L.

Solution

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(From Unit 1, Lesson 13.)