Five-Minute Check (over Lesson 7–5)
Then/Now
New Vocabulary
Key Concept: Types of Dilations
Example 1: Identify a Dilation and Find Its Scale Factor
Example 2: Real-World Example: Find and Use a Scale
Factor
Example 3: Verify Similarity after a Dilation
You identified congruence transformations.
(Lesson 4–7)
• Identify similarity transformations.
• Verify similarity after a similarity
transformation.
• dilation
• similarity transformation
• center of dilation
• scale factor of a dilation
• enlargement
• reduction
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.
2 or __
1.
Answer: So, the scale factor is __
4
2
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.
6 or 3.
Answer: So, the scale factor is __
2
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.
1
A. reduction; __
2
1
B. reduction; __
3
C. enlargement; 2
D. enlargement; 3
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.
2
A. reduction; __
3
1
B. reduction; __
3
3
C. enlargement; __
2
D. enlargement; 2
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.
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?
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
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)
1
A. __
2
1
B. __
3
3
C. __
2
3
D. __
4
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
1
B. __
3
C. 3
D. 4