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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 X
Point upper X

Point W
Point upper W

Point Y
Point upper Y

Point Z

1 answer

To determine which point of the figure will end up in Quadrant I after reflecting quadrilateral WXYZ across the y-axis, we first 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 \((-x, y)\).

  1. Point W: \((-2, 1)\) reflects to \((2, 1)\)
  2. Point X: \((-4, -3)\) reflects to \((4, -3)\)
  3. Point Y: \((5, -2)\) reflects to \((-5, -2)\)
  4. Point Z: \((6, 6)\) reflects to \((-6, 6)\)

Now, let's analyze the new coordinates to identify which point lands in Quadrant I (where both x and y are positive):

  • Point W: \((2, 1)\) - Quadrant I
  • Point X: \((4, -3)\) - Quadrant IV
  • Point Y: \((-5, -2)\) - Quadrant III
  • Point Z: \((-6, 6)\) - Quadrant II

Only Point W, which reflects to \((2, 1)\), ends up in Quadrant I.

Thus, the correct response is:

Point W