Question

A coordinate plane's axes range from negative 6 to 6, both by 1-unit increments. Points upper L, upper O, and upper W are plotted and connected via lines that form a triangle.
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 II
Quadrant II

Quadrant IV
Quadrant IV

Quadrant III
Quadrant III

Quadrant I
Quadrant I

Answer 1

To determine which quadrant ΔLOW will be in after the two reflections (across the y-axis and then the x-axis), we can analyze the transformations step by step.

1. **Reflection across the y-axis**: This transformation changes the x-coordinates of the points. If a point \((x, y)\) is reflected across the y-axis, it will become \((-x, y)\).
- This means points originally in Quadrant I will move to Quadrant II.
- Points in Quadrant II will move to Quadrant I.
- Points in Quadrant III will move to Quadrant IV.
- Points in Quadrant IV will move to Quadrant III.

2. **Reflection across the x-axis**: After reflecting across the y-axis, if a point is in the form \((-x, y)\), reflecting it across the x-axis will change its y-coordinate to \((-y)\).
- So, if the result from the first reflection is:
- Quadrant I becomes Quadrant IV,
- Quadrant II becomes Quadrant III,
- Quadrant III becomes Quadrant II,
- Quadrant IV becomes Quadrant I.

Now, depending on the original location of ΔLOW in the first quadrant, we can determine its final location:

- If the triangle is originally in Quadrant I:
- After reflecting across the y-axis: it goes to Quadrant II.
- After reflecting across the x-axis: it goes to Quadrant III.

Thus, the triangle ΔLOW will end up in **Quadrant III** after both reflections.

The final answer is **Quadrant III**.