Question

tiana will dilate rectangle abcd shown below using the rule (x, y) → (0.8x, 0.8y). mark each statement in 13 - 15 as true or false, and correct any false statements. 13. abcd will be smaller than abcd. 14. a will be located at (8, 4). 15. the orientation of the figure changed.

Explanation:

Step1: Analyze the transformation rule

The rule $(x,y)\to(0.8x, 0.8y)$ is a dilation with a scale - factor of $0.8$. Since $0 < 0.8<1$, the new figure $A'B'C'D'$ will be smaller than the original figure $ABCD$. So, the statement "A'B'C'D' will be smaller than ABCD" is True.

Step2: Find the coordinates of $A'$

From the graph, the coordinates of $A$ are $(10, 5)$. Using the transformation rule $(x,y)\to(0.8x, 0.8y)$, for point $A$: $x = 10$ and $y = 5$. Then $x'=0.8\times10 = 8$ and $y'=0.8\times5 = 4$. So, $A'$ is located at $(8,4)$. The statement "A' will be located at (8, 4)" is True.

Step3: Analyze the orientation

A dilation is a non - rigid transformation that changes the size of a figure but not its shape or orientation. So, the statement "The orientation of the figure changed" is False.

Answer:

1. True
2. True
3. False