Question

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

Answer 1

Answer: The correct option is (a).

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.

Answer 2

The answer would be a