Making Predictions with Transformations Quick Check 4 of 54 of 5 Items Question Use the image to answer the question. Which quadrant will ΔLOW be in when it is reflected across the y-axis and then reflected across the x-axis? (1 point) Responses Quadrant III Quadrant III Quadrant IV Quadrant IV Quadrant II Quadrant II Quadrant I Quadrant I Skip to navigation

Answer 1

To determine the position of ΔLOW after the specified reflections, we need to analyze the transformations step by step.

1. Reflection across the y-axis: When a point (x, y) is reflected across the y-axis, its x-coordinate changes sign, resulting in the point (-x, y). This reflection switches the position of the triangle from one side of the y-axis to the other.

2. Reflection across the x-axis: When a point (x, y) is reflected across the x-axis, its y-coordinate changes sign, resulting in the point (x, -y). This reflection switches the position of the triangle above and below the x-axis.

Let's consider where ΔLOW could initially be positioned:

• If ΔLOW was initially in Quadrant I (where x > 0 and y > 0), it would be reflected across the y-axis to Quadrant II (where x < 0 and y > 0) and then across the x-axis to Quadrant III (where x < 0 and y < 0).
• If it was in Quadrant II, it would go to Quadrant I after the y-axis reflection and then to Quadrant IV after the x-axis reflection.
• If it was in Quadrant III, it would go to Quadrant IV and then to Quadrant I after the reflections.
• If it was in Quadrant IV, it would go to Quadrant III and then to Quadrant II after the transformations.

Considering these transformations, if ΔLOW is reflected across the y-axis and then the x-axis, it ends up in Quadrant III.

Thus, the answer is Quadrant III.