Question

After rotating ABC 180° about the origin and then reflecting it over the x-axis, what are the coordinates of A''B''C''?

A) A''(2, 6), B''(5, 4), C''(2, 1)
B) A''(6, 2), B''(4, 5), C''(1, 2)
C) A''(-2, 6), B''(5, 4), C''(-2, 1)
D) A''(6, -2), B''(4, -5), C''(1, -2)

Answer 1

After rotating ABC 180° about the origin and then reflecting it over the x-axis, the coordinates of A''B''C'' can be found by applying the transformations to the original coordinates of A, B, and C.

Step-by-step explanation:

After rotating ABC 180° about the origin and then reflecting it over the x-axis, the coordinates of A''B''C'' can be found by applying the transformations to the original coordinates of A, B, and C.

Let A(x, y) be the coordinates of point A, where x represents the x-coordinate and y represents the y-coordinate. After rotating 180° about the origin, the new coordinates of A' are (-x, -y). After reflecting over the x-axis, the new coordinates of A'' are (-x, -(-y)) which simplifies to (-x, y).

Similarly, the new coordinates of B'' and C'' can be found by applying the same transformations to the original coordinates of B and C. Therefore, the correct coordinates of A''B''C'' are A''(-x1, y1), B''(-x2, y2), C''(-x3, y3), where x1, x2, x3, y1, y2, and y3 represent the original x and y coordinates of A, B, and C respectively.