Use the image to answer the question.

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 W
Point upper W

Point X
Point upper X

Point Y
Point upper Y

Point Z

Answer 1

To determine which point will end up in Quadrant I after the quadrilateral WXYZ is reflected across the y-axis, we need to reflect each point individually.

The reflection across the y-axis changes the x-coordinate of each point to its opposite value (i.e., \((x, y) \to (-x, y)\)).

Let's reflect each point:

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 \((-6, 6)\)

After reflecting these points:

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

The only point that ends up in Quadrant I after the reflection is:

Point W.