Question

If triangle xyz is translated using the rule (x, y) → (x + 4, y - 1) and then reflected across the y-axis to create triangle x'y'z', what is the location of x'?

1) (-4, 1)
2) (4, -1)
3) (-8, 4)
4) (8, -4)

Answer 1

The location of point x' is the result of applying a translation and a reflection across the y-axis to the original point x. After applying the given rules of transformation, the correct location for point x' is (-8, 2), which corresponds to option 3.

Step-by-step explanation:

The question involves finding the location of point x' after performing a series of transformations on triangle xyz.

Firstly, a translation using the rule (x, y) → (x + 4, y - 1) is applied and then a reflection across the y-axis.

Let's assume the original coordinates of point x are (x1, y1).

After the translation, the coordinates become (x1 + 4, y1 - 1).

The reflection across the y-axis will then change the x-coordinate to its negative value, resulting in (-x1 - 4, y1 - 1).

To find the location of x', we look for the option that matches this transformation outcome.

• (-4, 1) does not include a translation.
• (4, -1) is only the translation without reflection.
• (-8, 2) could be if the original point was (x1, y1) = (4, 3) before transformations.
• (8, -4) shows a positive x-coordinate after reflection, which is incorrect.

Therefore, option 3 is the correct location of x' because it reflects the final x-coordinate being negative and accounting for both transformations.