Question

question 5 (3 points) choose all the rules that represent a dilation of a shape increasing in size (getting bigger). dilations involve similar shapes. □a (4.5x,4.5y) □b (0.5x,0.5y) □c (\frac{4}{5}x,\frac{4}{5}y) □d (\frac{6}{5}x,\frac{6}{5}y) □e (-2x,-2y) □f (4x,2y) □g (2x,2y)

Explanation:

Step1: Recall dilation rule

In a dilation $(kx, ky)$ about the origin, if $|k|> 1$, the shape increases in size.

Step2: Analyze option a

For $(4.5x,4.5y)$, $k = 4.5$ and $|4.5|>1$, so it represents an increasing - size dilation.

Step3: Analyze option b

For $(0.5x,0.5y)$, $k = 0.5$ and $|0.5|<1$, so it represents a decreasing - size dilation.

Step4: Analyze option c

For $(\frac{4}{5}x,\frac{4}{5}y)$, $k=\frac{4}{5}=0.8$ and $|0.8|<1$, so it represents a decreasing - size dilation.

Step5: Analyze option d

For $(\frac{6}{5}x,\frac{6}{5}y)$, $k=\frac{6}{5} = 1.2$ and $|1.2|>1$, so it represents an increasing - size dilation.

Step6: Analyze option e

For $(- 2x,-2y)$, $|k| = |-2|=2>1$, so it represents an increasing - size dilation (the negative sign just changes the orientation).

Step7: Analyze option f

For $(4x,2y)$, since the scale factors for $x$ and $y$ are $4$ and $2$ respectively and both $|4|>1$ and $|2|>1$, it represents an increasing - size dilation.

Step8: Analyze option g

For $(2x,2y)$, $k = 2$ and $|2|>1$, so it represents an increasing - size dilation.

Answer:

a. $(4.5x,4.5y)$
d. $(\frac{6}{5}x,\frac{6}{5}y)$
e. $(-2x,-2y)$
f. $(4x,2y)$
g. $(2x,2y)$