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 -5,-2, upper O -2, -4, and upper W -4, -6 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 I
Quadrant I

Quadrant II
Quadrant II

Quadrant III
Quadrant III

Quadrant IV
Quadrant IV
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Answer 1

To find out where ΔLOW will be after reflecting across the y-axis and then the x-axis, we first need to determine the coordinates of the vertices after the reflections.

1. **Original Points:**
- L(-5, -2)
- O(-2, -4)
- W(-4, -6)

2. **Reflection across the y-axis:**
- Reflection across the y-axis changes the sign of the x-coordinate:
- L becomes (5, -2)
- O becomes (2, -4)
- W becomes (4, -6)

3. **Reflection across the x-axis:**
- Reflection across the x-axis changes the sign of the y-coordinate:
- L becomes (5, 2)
- O becomes (2, 4)
- W becomes (4, 6)

4. **New Points after both reflections:**
- L(5, 2)
- O(2, 4)
- W(4, 6)

Now we can determine which quadrant these points lie in:
- All new points have positive x and y coordinates, which means they are located in **Quadrant I**.

Thus, ΔLOW will be in **Quadrant I** after both reflections.