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 I
Quadrant I

Quadrant III
Quadrant III

Quadrant II
Quadrant II

Quadrant IV

Answer 1

To determine the position of triangle ΔX'Y'Z' after reflecting triangle ΔXYZ across the y-axis and then the x-axis, we can follow the reflections step-by-step.

1. **Initial Position**: Triangle ΔXYZ is in Quadrant IV.

2. **Reflection across the y-axis**: When you reflect across the y-axis, the x-coordinates of all points change their signs while the y-coordinates remain unchanged. Therefore, points in Quadrant IV (where x > 0 and y < 0) will move to Quadrant III (where x < 0 and y < 0).

3. **Reflection across the x-axis**: Now, reflecting the newly positioned triangle (in Quadrant III) across the x-axis will change the signs of the y-coordinates while the x-coordinates remain unchanged. This means that the points will move from Quadrant III (where x < 0 and y < 0) to Quadrant II (where x < 0 and y > 0).

Thus, after both reflections, triangle ΔX'Y'Z' will be located in **Quadrant II**.

**Correct Answer: Quadrant II**