Question

A'B'C'D' is the image of ABCD . What transformation(s) would result in this image?

1. ABCD is reflected over the line y = x .
2. ABCD is dilated about the origin with a scale factor of -1.
3. ABCD is reflected across the y-axis and then the x-axis.
4. ABCD is rotated 180° around the origin.

Answer 1

3

Explanation:

All points are the same distance from the origin. What helps me is visualizing the transformation in my head, though another method is drawing it, or learning the numerical rules. Like for example, a reflection across the y axis goes from (x, y) to (-x, y).

Here's a process of elimination:

1) The resulting image is upside down

2) The preimage is originally the same size as the intended image, so it would be smaller, upside down, and still far away.

4) The resulting image is still far from the intended image.

Answer 2

Option 3 and 4.

Explanation:

From the given figure it is clear that the vertices of figure ABCD are A(3,-2), B(5,-5), C(3,-5) and D(2,-4).

The vertices of figure A'B'C'D' are A'(-3,2),B'(-5,5), C'(-3,5) and D'(-2,4).

The relation between preimage are image is

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

It means ABCD is rotated 180° around the origin.

If ABCD is reflected across the y-axis and then the x-axis.

Across the y-axis :
`(x,y)\rightarrow (-x,y)`

Across the x-axis :
`(x,y)\rightarrow (x,-y)`

Across the y-axis and then the x-axis :
`(x,y)\rightarrow (-x,-y)`.

Therefore, the correct options are 3 and 4.