Question

Triangle ABC is shown. A is at negative 5, 4. B is at negative 7, 2. C is at negative 2, 3.If triangle ABC is rotated 180 degrees, reflected over the y‐axis, and reflected over the x‐axis, where will point A' lie?

Answer 1

After rotating 180 degrees, reflecting over the y-axis, and the x-axis, point A' ends up in the same initial position at (-5, 4).

Step-by-step explanation:

Given that point A is initially at (-5, 4), let's apply the transformations step by step to determine the final position of point A' after rotating 180 degrees, reflecting over the y-axis, and reflecting over the x-axis.

• The rotation of 180 degrees about the origin will change the sign of both the x and y coordinates. Thus, after this rotation, point A will be at (5, -4).
• Reflecting this new point over the y-axis will invert the x-coordinate, giving us point A at (-5, -4).
• Finally, reflecting over the x-axis will invert the y-coordinate, resulting in point A' at (-5, 4), which is the same as the initial position.

Hence, point A' after all transformations will be located at (-5, 4).