Find the value of a. The triangles are similar. Find the value of n. Find the value of x. 5-Minute Check 1

Concept

B is smaller than A, so the dilation is a 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. Example 1

Answer: So, the scale factor is or . 1 2 4 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 . __ 1 2 4 Example 1

B is larger than A, so the dilation is an enlargement. 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. Example 1

Answer: So, the scale factor is or 3. 6 2 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. __ 6 2 Example 1

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 __ 1 3 2 Example 1

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 __ 1 3 2 Example 1

Answer: The enlarged receipt will be 3 inches by 8 inches. 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. Example 2

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 Example 2

original: M(–6, –3), N(6, –3), O(–6, 6) 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. Example 3

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. Example 3

original: G(2, 1), H(4, 1), I(2, 0), J(4, 0) 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) Example 3

Find and compare the ratios of corresponding sides. Verify Similarity after a Dilation Since the figures are rectangles, their corresponding angles are congruent. Find and compare the ratios of corresponding sides. Answer: Example 3

A. Graph the original figure and its dilated image 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. __ 1 2 3 4 Example 3

B. Graph the original figure and its dilated image 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 __ 1 3 Example 3