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.
-
Initial Position: Triangle ΔXYZ is in Quadrant IV.
-
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).
-
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
1 answer