Question

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Explanation:

5. Step1: Identify dilation type (reduction)

Figure B is smaller than Figure A, so it is a reduction.

5. Step2: Calculate scale factor

The side length of B is 1, side length of A is 2. $k = \frac{1}{2}$

6. Step1: Identify dilation type (enlargement)

Figure B is larger than Figure A, so it is an enlargement.

6. Step2: Calculate scale factor

The side length of B is 1, side length of A is $\frac{1}{2}$. $k = \frac{1}{\frac{1}{2}} = 2$

7. Step1: Identify dilation type (reduction)

Figure B is smaller than Figure A, so it is a reduction.

7. Step2: Calculate scale factor

The horizontal length of A is 4, horizontal length of B is 1. $k = \frac{1}{4}$

8. Step1: Identify dilation type (enlargement)

Figure B is larger than Figure A, so it is an enlargement.

8. Step2: Calculate scale factor

The side length of B is 6, side length of A is 3. $k = \frac{6}{3} = 2$

9. Step1: Divide R's coords by A's

Scale factor $k = \frac{9}{3} = \frac{12}{4} = 3$

10. Step1: Divide R's coords by A's

Scale factor $k = \frac{6}{9} = \frac{8}{12} = \frac{2}{3}$

11. Step1: Divide R's coords by A's

Scale factor $k = \frac{-10}{-2} = \frac{-15}{-3} = 5$

12. Step1: Dilate A(1,1) by k=2

$A'(1\times2, 1\times2) = (2,2)$

12. Step2: Dilate B(3,1) by k=2

$B'(3\times2, 1\times2) = (6,2)$

13. Step1: Dilate A(4,4) by $k=\frac{3}{4}$

$A'(4\times\frac{3}{4}, 4\times\frac{3}{4}) = (3,3)$

13. Step2: Dilate B(8,12) by $k=\frac{3}{4}$

$B'(8\times\frac{3}{4}, 12\times\frac{3}{4}) = (6,9)$

14. Step1: Dilate A(0,0) by k=5

$A'(0\times5, 0\times5) = (0,0)$

14. Step2: Dilate B(-3,2) by k=5

$B'(-3\times5, 2\times5) = (-15,10)$

Answer:

1. Reduction, $k=\frac{1}{2}$
2. Enlargement, $k=2$
3. Reduction, $k=\frac{1}{4}$
4. Enlargement, $k=2$
5. $k=3$
6. $k=\frac{2}{3}$
7. $k=5$
8. $A'(2,2)$, $B'(6,2)$
9. $A'(3,3)$, $B'(6,9)$
10. $A'(0,0)$, $B'(-15,10)$