Triangle A’B’C’ is the image of triangle ABC. Which transformations could have been used to create A’B’C’ ? Choose all that apply.1. a 180 degree rotation about the origin and then a translation 3 units up and 1 unit left2. a translation 3 units up and 1 unit left and then a 180 degree rotation about the origin3. a 90 degree clockwise rotation about the origin and then a reflection over the y-axis4. a 90 degree counterclockwise rotation about the origin and then a reflection over the x-axis 4. a translation 3 units down and 1 unit right and then a 180 degree rotation about the origin

Question
Answer:
Point A, initially at (-4, -1), moves to A' at (3, 4).
Point B (-5, -5) moves to B' (4, 8).
Point C (-3, -4) moves to C' (2, 7).
The first choice: rotating 180 degrees about the origin changes to sign of both x- and y-coordinates, so A(-4, -1) goes to (4, 1). Moving 3 up goes to (4, 4), and 1 left is (3, 4). For B(-5, -5), rotating brings it to (5, 5), up 3 to (5, 8), 1 left to (4, 8). For C(-3, -4), rotate to (3, 4), up 3 to (3, 7), 1 left to (2, 7). So since all points match up, this first choice is a correct answer.
The second choice does not work since: translating A 3 up and 1 left brings it to (-5, 2), and rotating it 180 degrees would then put A' at (5, -2).
The third choice: rotating A 90 degrees clockwise puts it at (-1, 4), and reflecting it over the y-axis puts it at (1, 4).
The fourth choice: rotation A 90 degrees counterclockwise puts it at (1, -4), and reflecting it over the x-axis puts it at (1, 4).
The fifth choice: translating 3 down and 1 right puts A at (-3, -4), then a 180-degree rotation puts it at (3, 4). B(-5, -5) translated goes to (-4, -8), and rotating brings it to  (4, 8). C(-3, -4) is translated to (-2, -7), and rotating puts it at (2, 7). So since all points match up, this choice is another correct answer.

So the possible transformations are the 1st and 5th choices.
solved
general 10 months ago 2503