Question

a four sided figure WXYZ is shown on the coordinate plane. The figure is then reflected across the y-axis. Which point of the figure above will end up in Quadrant I?

point y: (5, -2)
point x: (-4, -3)
point w: (-2, 1)

a. point X
b. point Z
c. point Y
d. point W

Answer 1

To determine which point of the figure will end up in Quadrant I after being reflected across the y-axis, we need to look at the coordinates of each point before the reflection:

1. **Point Y**: (5, -2)
2. **Point X**: (-4, -3)
3. **Point W**: (-2, 1)

When a point \((a, b)\) is reflected across the y-axis, its new coordinates will be \((-a, b)\).

Now, let’s reflect each point across the y-axis:

- **Point Y (5, -2)**: Reflects to \((-5, -2)\)
- **Point X (-4, -3)**: Reflects to \((4, -3)\)
- **Point W (-2, 1)**: Reflects to \((2, 1)\)

Next, we will check the new coordinates of each point to see which one falls in Quadrant I. Quadrant I is where both the x-coordinate and y-coordinate are positive:

- **Point Y after reflection**: \((-5, -2)\) → Negative x and negative y (not in Quadrant I)
- **Point X after reflection**: \((4, -3)\) → Positive x and negative y (not in Quadrant I)
- **Point W after reflection**: \((2, 1)\) → Positive x and positive y (is in Quadrant I)

Therefore, the point that ends up in Quadrant I after reflecting across the y-axis is **Point W**.

The answer is: **d. point W**.