Which quadrant will ΔX′Y′Z′

Question

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