Question

coordinate transformations

1. a figure is reflected across the x - axis.

which statement(s) about the resulting image are true?
check all that apply:
a. (x,y)→(x, - y)
b. (x,y)→(-x,y)
c. (x,y)→(-x, - y)
d. the image is reduced.
e. the figures are congruent.
f. (x,y)→(1/x,1/y)
g. (x,y)→(-1/x,1/y)
h. (x,y)→(1/x, - 1/y)
i. the image is enlarged.
j. the figures are similar.
explain your choice(s):

1. a figure is dilated by a scale factor of 2.

which statement(s) about the resulting image are true?
check all that apply:
a. (x,y)→(2x,2y)
b. (x,y)→(2x,y)
c. (x,y)→(x,2y)
d. the image is reduced.
e. the figures are congruent.
f. (x,y)→(-2x, - 2y)
g. (x,y)→(-2x,y)
h. (x,y)→(x, - 2y)
i. the image is enlarged.
j. the figures are similar.
explain your choice(s):

Explanation:

Step1: Recall reflection rule

When a figure is reflected across the x - axis, the x - coordinate remains the same and the y - coordinate changes sign. So the transformation rule is $(x,y)\to(x, - y)$. Also, a reflection is a rigid transformation which preserves the size and shape of the figure, so the pre - image and image are congruent and similar.

Step2: Recall dilation rule

When a figure is dilated by a scale factor of $k$, the transformation rule is $(x,y)\to(kx,ky)$. Here $k = 2$, so the rule is $(x,y)\to(2x,2y)$. A dilation with a scale factor $k>1$ (in this case $k = 2$) enlarges the figure, and the pre - image and image are similar but not congruent.

Answer:

1.
a. $(x,y)\to(x, - y)$
e. The figures are congruent
j. The figures are similar
2.
a. $(x,y)\to(2x,2y)$
i. The image is enlarged
j. The figures are similar