Question

Which Quadrant will triangle LAW be in when it is reflected across the y-axis and then reflected across the x-axis?
Triangle LOW
Point L: (-5, -2)
Point O: (-2, -4)
Point W: (-4, -6)

A. Quadrant III
B. Quadrant II
C. Quadrant IV
D. Quadrant I

Answer 1

To find out which quadrant triangle LAW will be in after the specified reflections, we need to perform the reflections step by step on each point of the triangle.

1. **Reflection across the y-axis**:
When a point \((x, y)\) is reflected across the y-axis, its new coordinates become \((-x, y)\).

- Point L: from \((-5, -2)\) to \((5, -2)\)
- Point O: from \((-2, -4)\) to \((2, -4)\)
- Point W: from \((-4, -6)\) to \((4, -6)\)

After reflecting across the y-axis, the points are:
- L: \((5, -2)\)
- O: \((2, -4)\)
- W: \((4, -6)\)

2. **Reflection across the x-axis**:
Next, when a point \((x, y)\) is reflected across the x-axis, its new coordinates become \((x, -y)\).

- Point L: from \((5, -2)\) to \((5, 2)\)
- Point O: from \((2, -4)\) to \((2, 4)\)
- Point W: from \((4, -6)\) to \((4, 6)\)

After reflecting across the x-axis, the points are:
- L: \((5, 2)\)
- O: \((2, 4)\)
- W: \((4, 6)\)

Now let's determine the quadrant for each point:

- Point L: \((5, 2)\) is in Quadrant I (x > 0, y > 0)
- Point O: \((2, 4)\) is in Quadrant I (x > 0, y > 0)
- Point W: \((4, 6)\) is in Quadrant I (x > 0, y > 0)

All the points of triangle LAW after both reflections are in Quadrant I. Thus, the answer is:

**D. Quadrant I**