Question

Which statement is true about figures ABCD and A′B′C′D′? (1 point)

A polygon ABCD has A at ordered pair 2, negative 2, B at 1, negative 4, C at 0 and negative 2, D at 1 and negative 1. A polygon A prime B prime C prime D prime has A prime at ordered pair negative 2, negative 2, B prime at ordered pair negative 1, negative 4, C prime at ordered pair 0, negative 2 and D prime at ordered pair negative 1, negative 1.
Select one:
a. A′B′C′D′ is obtained by rotating ABCD counterclockwise by 180 degrees about the origin and then reflecting it across the x-axis.
b. A′B′C′D′ is obtained by translating ABCD 2 units up and then reflecting it about the y-axis. Incorrect
c. A′B′C′D′ is obtained by translating ABCD 2 units up and then reflecting it about the x-axis.
d. A′B′C′D′ is obtained by rotating ABCD counterclockwise by 180 degrees about the origin and then reflecting it across the y-axis.

Answer 1

The answer would be a

Answer 2

Answer: The correct option is (a).

Step-by-step explanation:

It is given that A(2,-2) , B(1,-4), C(0,-2), D(1,-1), A'(-2,-2), B'(-1,-4), C'(0,-2), D'(-1,-1).

From the given information we can conclude that if the coordinates of preimage is in the form of (x,y), then the coordinates of the image is (-x,y).

If ABCD counterclockwise by 180 degrees about the origin, then

`(x,y)\rightarrow (-x,-y)`

After that it is reflecting it across the x-axis, then the sign of y coordinates changes.

`(x,y)\rightarrow (-x,y)`

It is same as the form that we conclude from the given information. Therefore the option (a) is correct.

Since the absolute values of the coordinates are same only sign are different, therefore the translation can not be applied to get the image. So option (b) and (c) are incorrect.

If ABCD counterclockwise by 180 degrees about the origin, then

`(x,y)\rightarrow (-x,-y)`

After that it is reflecting it across the y-axis, then the sign of x coordinates changes.

`(x,y)\rightarrow (x,-y)`

Which can not satisfies the coordinates of image and preimage, therefore option (d) is incorrect.