Question

c. what is the scale factor that takes figure 1 to figure 2?
d. g and h are two points on figure 1, but they are not shown. the distance between g and h is 1. what is the distance between the corresponding points on figure 2?
problem 4
to make 1 batch of lavender paint, the ratio of cups of pink paint to cups of blue paint is 6 to 5. find two more ratios of cups of pink paint to cups of blue paint that are equivalent to this ratio.

Explanation:

Step - by - Step Format

Step1: Find the scale factor (for part c)

Let's assume we know the corresponding side - lengths of Figure 1 and Figure 2. If the length of a side in Figure 1 is $a$ and the length of the corresponding side in Figure 2 is $b$, the scale factor $k$ from Figure 1 to Figure 2 is given by the formula $k=\frac{b}{a}$. Without specific side - length values, we'll just use the concept. If we assume we have measured the side - lengths and found that a side of length $x$ in Figure 1 corresponds to a side of length $y$ in Figure 2, then the scale factor $k = \frac{y}{x}$.

Step2: Find the distance between corresponding points (for part d)

The distance between corresponding points in two similar figures is related to the scale factor. If the scale factor from Figure 1 to Figure 2 is $k$, and the distance between two points $G$ and $H$ in Figure 1 is $d_1 = 1$, then the distance $d_2$ between the corresponding points in Figure 2 is given by $d_2=k\times d_1$. Since $d_1 = 1$, the distance between the corresponding points in Figure 2 is equal to the scale factor $k$.

Step3: Find equivalent ratios (for Problem 4)

To find equivalent ratios of $\frac{6}{5}$, we can multiply both the numerator and the denominator by the same non - zero number.
If we multiply by 2, we get $\frac{6\times2}{5\times2}=\frac{12}{10}$.
If we multiply by 3, we get $\frac{6\times3}{5\times3}=\frac{18}{15}$.

Answer:

c. The scale factor is found by dividing the length of a side in Figure 2 by the length of the corresponding side in Figure 1.
d. The distance between the corresponding points is equal to the scale factor.
Problem 4: Two equivalent ratios are $\frac{12}{10}$ and $\frac{18}{15}$.