Question

Which quadrant will ΔX′Y′Z′
be in if ΔXYZ
begins in Quadrant IV and is reflected across the y-axis and then the x-axis?(1 point)
Responses

Quadrant IV
Quadrant IV

Quadrant I
Quadrant I

Quadrant II
Quadrant II

Quadrant III

Answer 1

To understand the position of triangle \( \Delta X'Y'Z' \) after the transformations given to triangle \( \Delta XYZ \), we need to analyze the reflection process step by step.

1. **Initial Position**: Triangle \( \Delta XYZ \) starts in Quadrant IV. In this quadrant, the x-coordinates are positive, and the y-coordinates are negative.

2. **Reflection Across the y-axis**:
- Reflecting across the y-axis changes the sign of the x-coordinates. So the points in Quadrant IV will move to Quadrant III because now the x-coordinates will be negative, and the y-coordinates remain negative.

3. **Reflection Across the x-axis**:
- Reflecting across the x-axis changes the sign of the y-coordinates. So the points in Quadrant III, which have negative y-coordinates, will move to Quadrant II, where y-coordinates are positive, but x-coordinates remain negative.

Therefore, after both reflections, \( \Delta X'Y'Z' \) will be in **Quadrant II**.

The correct response is:

**Quadrant II**