Question

A point is first reflected over the y-axis, then rotated 180 degrees counterclockwise around the origin. If its original coordinates were (2, -3), what are its final coordinates?

Answer 1

Let's start with the original point, which is \((2, -3)\).

1. **Reflecting over the y-axis:**
When a point \((x, y)\) is reflected over the y-axis, its x-coordinate changes sign, while the y-coordinate remains the same.

So, reflecting \((2, -3)\) over the y-axis gives us:
\[
(-2, -3)
\]

2. **Rotating 180 degrees counterclockwise around the origin:**
To rotate a point \((x, y)\) by 180 degrees around the origin, you negate both the x and y coordinates.

Thus, rotating the point \((-2, -3)\) gives us:
\[
(2, 3)
\]

Therefore, the final coordinates after reflecting over the y-axis and then rotating 180 degrees counterclockwise around the origin are:
\[
\boxed{(2, 3)}
\]