Question

Point A is at (-2,6). First, rotate the point 180 degrees around the origin, then reflect it over the X-axis. What is the new location A"?

a) (-2, -6)
b) (2, -6)
c) (2, 6)
d) (-2, 6)

Answer 1

After rotating point A (-2, 6) by 180 degrees and reflecting it over the X-axis, the new location of point A" is (2, 6), which is option c).

Step-by-step explanation:

The student's question involves rotating a point in the coordinate system and then reflecting it over an axis. To find the new location of point A after a 180-degree rotation around the origin and a reflection over the X-axis, we perform these transformations step by step:

1. 180-degree rotation: Rotating the point (-2, 6) around the origin by 180 degrees will change the sign of both coordinates, resulting in the point (2, -6).
2. Reflection over the X-axis: Reflecting the point (2, -6) over the X-axis will change the sign of the Y-coordinate while leaving the X-coordinate unchanged, giving us the point (2, 6).

Therefore, the new location of A" after these transformations is (2, 6), which corresponds to option c).