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An illustration shows a coordinate plane. The x-axis and the y-axis range from negative 6 to 6 in one unit increments. Four points are plotted. The points are connected to form a quadrilateral. Point W is plotted at the coordinates left parenthesis negative 2 comma 1 right parenthesis, Point X is plotted at left parenthesis negative 4 comma negative 3 right parenthesis, point Y is plotted at left parenthesis 5 comma negative 2 right parenthesis, and point Z is plotted at left parenthesis 6 comma 6 right parenthesis. Points W and X, points X and Y, points Y and Z, and points Z and W are connected by line segments to form quadrilateral W X Y Z.

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 z
point w
point x
point y

1 answer

To determine which point will end up in Quadrant I after reflecting the quadrilateral WXYZ across the y-axis, we need to find the new coordinates of each point after the reflection.

The rule for reflecting a point \((x, y)\) across the y-axis is \((-x, y)\).

  1. Point W:

    • Original coordinates: \((-2, 1)\)
    • After reflection: \((2, 1)\)

  2. Point X:

    • Original coordinates: \((-4, -3)\)
    • After reflection: \((4, -3)\)

  3. Point Y:

    • Original coordinates: \((5, -2)\)
    • After reflection: \((-5, -2)\)

  4. Point Z:

    • Original coordinates: \((6, 6)\)
    • After reflection: \((-6, 6)\)

Now let's analyze the new coordinates:

  • Point W: \((2, 1)\) - This point is in Quadrant I (positive x and positive y).
  • Point X: \((4, -3)\) - This point is in Quadrant IV (positive x and negative y).
  • Point Y: \((-5, -2)\) - This point is in Quadrant III (negative x and negative y).
  • Point Z: \((-6, 6)\) - This point is in Quadrant II (negative x and positive y).

Therefore, the point that will end up in Quadrant I after the reflection is Point W.