Question

Given the preimage and image,find the dilation scale factor.​

Answer 1

Answer:

The dilation scale factor is $\frac{1}{2}$.

Step-by-step explanation:

The image is the dilated form of its preimage if and only if the following conditions are observed:

1) $K' = \alpha_{1} \cdot K$

2) $T' = \alpha_{2} \cdot T$

3) $P' = \alpha_{3} \cdot P$

4) $J' = \alpha_{4} \cdot J$

5) $\alpha_{1} = \alpha_{2} = \alpha_{3} = \alpha_{4}$

If we know that $K = (2, 0)$, $K' = (1, 0)$, $T = (3, 0)$, $T' = (1.5,0)$, $P = (1, 5)$, $P' = (0.5, 2.5)$, $J = (0, 3)$ and $J' = (0, 1.5)$, then the coefficients are, respectively:

$\alpha_{1} = \frac{1}{2}$, $\alpha_{2} = \frac{1}{2}$, $\alpha_{3} = \frac{1}{2}$, $\alpha_{4} = \frac{1}{2}$

As $\alpha_{1} = \alpha_{2} = \alpha_{3} = \alpha_{4}$, we conclude that the dilation scale factor applied in the preimage is equal to $\frac{1}{2}$.