Question
se 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 Z
Point upper Z
Point W
Point upper W
Point Y
Point upper Y
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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?
(1 point)
Responses
Point X
Point upper X
Point Z
Point upper Z
Point W
Point upper W
Point Y
Point upper Y
Skip to navigation
Answers
GPT-4o mini
To determine which point of the quadrilateral WXYZ will end up in Quadrant I after being reflected across the y-axis, we need to find the coordinates of each point after reflection.
Reflecting a point \((x, y)\) across the y-axis results in the point \((-x, y)\).
The original coordinates of the points are:
- Point W: \((-2, 1)\)
- Point X: \((-4, -3)\)
- Point Y: \((5, -2)\)
- Point Z: \((6, 6)\)
Now reflecting each point:
- Point W: \((-(-2), 1) = (2, 1)\)
- Point X: \((-(-4), -3) = (4, -3)\)
- Point Y: \((-5, -2) = (-5, -2)\)
- Point Z: \((-6, 6) = (-6, 6)\)
Next, we identify in which quadrant each reflected point is located:
- Point W: \((2, 1)\) is in Quadrant I (positive x and 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).
Since Point W \((2, 1)\) is the only point that ends up in Quadrant I after reflection, the correct answer is:
**Point W**
Reflecting a point \((x, y)\) across the y-axis results in the point \((-x, y)\).
The original coordinates of the points are:
- Point W: \((-2, 1)\)
- Point X: \((-4, -3)\)
- Point Y: \((5, -2)\)
- Point Z: \((6, 6)\)
Now reflecting each point:
- Point W: \((-(-2), 1) = (2, 1)\)
- Point X: \((-(-4), -3) = (4, -3)\)
- Point Y: \((-5, -2) = (-5, -2)\)
- Point Z: \((-6, 6) = (-6, 6)\)
Next, we identify in which quadrant each reflected point is located:
- Point W: \((2, 1)\) is in Quadrant I (positive x and 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).
Since Point W \((2, 1)\) is the only point that ends up in Quadrant I after reflection, the correct answer is:
**Point W**