Question

Which of the following statements is true? Square A'B'C'D' is the image of square ABCD after a dilation and a rotation. Square A'B'C'D' is the image of square ABCD after a reflection and a dilation. Square A'B'C'D'is the image of ABCD after a reflection and a translation Square A'B'C'D' is the image of ABCD after a rotation.

Answer 1

Square A'B'C'D' is the image of ABCD after a reflection and a translation

Step-by-step explanation:

Given the quadrilateral ABCD, with coordinates;

`(-2,9),(-7,9),(-7,4),(-2,4)`

From the given image A'B'C'D', the size of the image and that of the pre-image is the same so, there is no dilation since there is no change in size.

Looking at the orientation of the image, we can observe the pre-image was reflected across the x-axis;

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

Looking further, we can see that there has been a shift in the position of the image after the reflection. So, there is also a translation after the reflection.

Therefore, Square A'B'C'D' is the image of ABCD after a reflection and a translation