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Use the image to answer the question.

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?

(1 point)
Responses

Point Y
Point upper Y

Point Z
Point upper Z

Point W
Point upper W

Point X
Point upper X
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1 answer

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

The reflection of a point \((x, y)\) across the y-axis results in the new coordinates \((-x, y)\).

Now, let's reflect each of the points:

  1. Point W: Original coordinates: \((-2, 1)\)
    Reflected coordinates: \((-(-2), 1) = (2, 1)\)

  2. Point X: Original coordinates: \((-4, -3)\)
    Reflected coordinates: \((-(-4), -3) = (4, -3)\)

  3. Point Y: Original coordinates: \((5, -2)\)
    Reflected coordinates: \((-5, -2)\)

  4. Point Z: Original coordinates: \((6, 6)\)
    Reflected coordinates: \((-6, 6)\)

Now, we check the reflected points to see which one ends up in Quadrant I, where both x and y coordinates are positive:

  • Point W after reflection: \((2, 1)\) - Quadrant I (both coordinates positive)
  • Point X after reflection: \((4, -3)\) - Quadrant IV (x positive, y negative)
  • Point Y after reflection: \((-5, -2)\) - Quadrant III (both coordinates negative)
  • Point Z after reflection: \((-6, 6)\) - Quadrant II (x negative, y positive)

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

Answer: Point W