Question

Use the image to answer the 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 IV
Quadrant IV

Quadrant III
Quadrant III

Quadrant II
Quadrant II

Quadrant I

Answer 1

To determine the quadrant of triangle ΔLOW after reflecting it first across the y-axis and then across the x-axis, we can use the properties of reflections.

1. **Reflecting across the y-axis**: When points are reflected across the y-axis, the x-coordinates of the points change sign, while the y-coordinates remain the same. So if the original points (L, O, W) have coordinates (x, y), after reflection across the y-axis, they become (-x, y).

2. **Reflecting across the x-axis**: After reflecting across the y-axis, the new points (-x, y) will be reflected across the x-axis. This means the y-coordinates will change sign, leading to the points becoming (-x, -y).

Now we just need to remember the quadrant system on a coordinate plane:
- Quadrant I: (+, +)
- Quadrant II: (-, +)
- Quadrant III: (-, -)
- Quadrant IV: (+, -)

After performing the two reflections, the points of ΔLOW that were originally in one of the quadrants will end up in Quadrant III because both x and y will be negative.

Therefore, the answer is:

**Quadrant III**