Question

AABC has vertices A(0, -1), B(3, 4), and C(3, 1). Rotate AABC 180° about the origin and then reflect it across the x-axis. ​

Answer 1

To rotate AABC 180° about the origin and then reflect it across the x-axis, switch the signs of the x and y coordinates to rotate and change the sign of the y-coordinate to reflect.

Step-by-step explanation:

To rotate a point (x, y) by 180° about the origin, you switch the signs of the x and y coordinates to get (-x, -y). Applying this to each vertex of AABC, we get A'(-0, 1), B'(-3, -4), and C'(-3, -1).

To reflect a point across the x-axis, you keep the x-coordinate the same and change the sign of the y-coordinate. Applying this to each vertex of the rotated AABC, we get A''(-0, -1), B''(-3, 4), and C''(-3, 1).

Therefore, the final vertices of the rotated and reflected AABC are: A''(0, -1), B''(3, -4), and C''(3, -1).1