Question

state whether a dilation with the given scale factor is a reduction or an enlargement.1. $k=3$2. $k=1$3. $k=\frac{5}{4}=1\frac{1}{4}$4. $k=0.83$determine whether the dilation from figure a to figure b is a reduction or an enlargement. then find its scale factor.5.6.7.8.

Explanation:

Step1: Analyze Figure 5 (A→B)

Figure B is smaller than A, so it's a reduction. Take a side of A: length = 4 units. Side of B: length = 2 units. Scale factor $k=\frac{2}{4}=\frac{1}{2}$

Step2: Analyze Figure 6 (A→B)

Figure B is larger than A, so it's an enlargement. Take a side of A: length = 2 units. Side of B: length = 4 units. Scale factor $k=\frac{4}{2}=2$

Step3: Analyze Figure 7 (A→B)

Figure B is smaller than A, so it's a reduction. Take a side of A: length = 4 units. Side of B: length = 2 units. Scale factor $k=\frac{2}{4}=\frac{1}{2}$

Step4: Analyze Figure 8 (A→B)

Figure B is larger than A, so it's an enlargement. Take a side of A: length = 2 units. Side of B: length = 4 units. Scale factor $k=\frac{4}{2}=2$

Answer:

1. Reduction, $k=\frac{1}{2}$
2. Enlargement, $k=2$
3. Reduction, $k=\frac{1}{2}$
4. Enlargement, $k=2$