Over Lesson 7–5

Find the value of a.

The triangles are similar.Find the value of n.

Find the value of x.

Identify a Dilation and Find Its Scale Factor

A. Determine whether the dilation from Figure A to Figure B is an enlargement or a reduction. Then find the scale factor of the dilation.

B is smaller than A, so the dilation is a reduction.

Identify a Dilation and Find Its Scale Factor

The distance between the vertices at (2, 2) and (2, –2)

for A is 4 and from the vertices at (1, 1) and (1, –1) for

B is 2.

Answer: So, the scale factor is or . __12

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Identify a Dilation and Find Its Scale Factor

B. Determine whether the dilation from Figure A to Figure B is an enlargement or a reduction. Then find the scale factor of the dilation.

B is larger than A, so the dilation is an enlargement.

Identify a Dilation and Find Its Scale Factor

The distance between the vertices at (3, 3) and (–3, 3) for A is 6 and from the vertices at (1, 1) and (–1, 1) for B is 2.

Answer: So, the scale factor is or 3. __62

A. Determine whether the dilation from Figure A to Figure B is an enlargement or a reduction. Then find the scale factor of the dilation.

A. reduction;

B. reduction;

C. enlargement; 2

D. enlargement; 3

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B. Determine whether the dilation from Figure A to Figure B is an enlargement or a reduction. Then find the scale factor of the dilation.

A. reduction;

B. reduction;

C. enlargement;

D. enlargement; 2

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Find and Use a Scale Factor

PHOTOCOPYING A photocopy of a receipt is 1.5 inches wide and 4 inches long. By what percent should the receipt be enlarged so that its image is 2 times the original? What will be the dimensions of the enlarged image? To enlarge the receipt 2 times the original, use a scale factor of 2. Written as a percent, the scale factor is (2 ● 100%) or 200%. Now, find the dimensions of the enlarged receipt.

width: 1.5 in. ● 200% = 3 in.

length: 4 in. ● 200% = 8 in.

Answer: The enlarged receipt will be 3 inches by 8 inches.

A. 15 inches by 25 inches

B. 8 inches by 15 inches

C. 12 inches by 22.5 inches

D. 16 inches by 30 inches

PHOTOGRAPHS Mariano wants to enlarge a picture he took that is 4 inches by 7.5 inches. He wants it to fit perfectly into a frame that is 400% of the original size. What will be the dimensions of the enlarged photo?

Verify Similarity after a Dilation

A. Graph the original figure and its dilated image. Then verify that the dilation is a similarity transformation.original: M(–6, –3), N(6, –3),

O(–6, 6)

image: D(–2, –1), F(2, –1), G(–2, 2)

Graph each figure. Since M and D are both right angles, M D. Show that the lengths of the sides that include M and D are proportional.

Verify Similarity after a Dilation

Use the coordinate grid to find the lengths of the vertical segments MO and DG and the horizontal segments MN and DF.

Answer: Since the lengths of the sides that include M and D are proportional, ΔMNO ~ ΔDFG by SAS Similarity.

Verify Similarity after a Dilation

B. Graph the original figure and its dilated image. Then verify that the dilation is a similarity transformation.original: G(2, 1), H(4, 1), I(2, 0), J(4, 0)

image: Q(4, 2), R(8, 2), S(4, 0), T(8, 0)

Verify Similarity after a Dilation

Since the figures are rectangles, their corresponding angles are congruent.

Find and compare the ratios of corresponding sides.

Answer:

A. Graph the original figure and its dilated image. Then determine the scale factor of the dilation.original: B(–7, –2), A(5, –2), D(–7, 7)image: J(–3, 0), K(1, 0), L(–3, 3)

A.

B.

C.

D.

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B. Graph the original figure and its dilated image. Then determine the scale factor of the dilation.original: A(4, 3), B(6, 3), C(4, 2), D(6, 2)image: E(6, 4), F(10, 4), G(6, 2), H(10, 2)

A. 2

B.

C. 3

D. 4

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