Question

If you reflect (–2, –8) across both axes, which quadrant will it be in? Justify your reasoning.

Answer 1

To reflect a point across both axes, we first reflect it across the y-axis and then reflect the result across the x-axis.

1. **Reflect across the y-axis:**
- The original point is \((-2, -8)\).
- When reflecting across the y-axis, the x-coordinate changes sign, while the y-coordinate remains the same.
- So, \((-2, -8)\) becomes \((2, -8)\).

2. **Reflect across the x-axis:**
- Now, we take the point \((2, -8)\) and reflect it across the x-axis.
- When reflecting across the x-axis, the y-coordinate changes sign, while the x-coordinate remains the same.
- Thus, \((2, -8)\) becomes \((2, 8)\).

The final point after reflecting \((-2, -8)\) across both axes is \((2, 8)\).

Next, let's determine in which quadrant the point \((2, 8)\) lies:

- The x-coordinate is positive (\(2 > 0\)).
- The y-coordinate is positive (\(8 > 0\)).

Since both coordinates are positive, the point \((2, 8)\) lies in the **first quadrant**.

Thus, after reflecting \((-2, -8)\) across both axes, the point will be in the **first quadrant**.