(02.02 MC) Triangle ABC is shown. A is at negative 2, 1. B is at negative 1, 4. C is at negative 4, 5. If triangle ABC is reflected over the x‐axis, reflected over the y‐axis, and rotated 180 degrees, where will point B' lie? (−1, 4) (1, −4) (4, −1) (−4, 1)

(-1,4)

Step-by-step explanation:

Point B in the pre-image is at (-1,4).

If triangle ABC is reflected over the x‐axis, the y-coordinate changes to its negative value, thus we have the transformation:

Next, if the point (-1,-4) is reflected over the y‐axis, the x-coordinate changes to its negative, Thus, we have the transformation:

Finally, a rotation by 180 degrees will give the coordinates of B' as:

The point B' will lie in (-1, 4) [ the same place as B].

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