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W(-2,1)

X(-4,-3)
Y(5,-2)
Z(6,6)

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?

(1 point)

Point X

Point Z

Point Y

Point W

1 answer

To determine which point of the figure WXYZ will end up in Quadrant I after being reflected across the y-axis, we first need to find the reflected coordinates of each point. When a point \((x, y)\) is reflected across the y-axis, its new coordinates become \((-x, y)\).

Let's reflect each point:

  • Point W (-2, 1): \[ \text{Reflected W: } (2, 1) \]

  • Point X (-4, -3): \[ \text{Reflected X: } (4, -3) \]

  • Point Y (5, -2): \[ \text{Reflected Y: } (-5, -2) \]

  • Point Z (6, 6): \[ \text{Reflected Z: } (-6, 6) \]

Now, we need to determine which of these reflected points lies in Quadrant I. A point is in Quadrant I if its \(x\) coordinate is positive and its \(y\) coordinate is positive.

  • Reflected W (2, 1): \(x = 2\) (positive), \(y = 1\) (positive) → Quadrant I
  • Reflected X (4, -3): \(x = 4\) (positive), \(y = -3\) (negative) → Not Quadrant I
  • Reflected Y (-5, -2): \(x = -5\) (negative), \(y = -2\) (negative) → Not Quadrant I
  • Reflected Z (-6, 6): \(x = -6\) (negative), \(y = 6\) (positive) → Not Quadrant I

The only point that ends up in Quadrant I is Point W after the reflection.

Thus, the answer is Point W.