A reflection can be thought of as "mirroring" or "flipping" an object over a line of reflection.
When a point is reflected in the -axis, the -coordinate remains the same, but the -coordinate is transformed into its opposite (i.e., its sign is changed). The following function can represent this transformation:
For example, reflecting the point in the -axis gives the point as shown below.
On the other hand, when a point is reflected in the -axis, the -coordinate remains the same, but the -coordinate is transformed into its opposite (its sign is changed). The following function can represent this transformation:
For example, reflecting the point in the -axis gives the point as shown below.
The point is reflected across the -axis. What are the coordinates of the resulting point?
Reflection across the -axis can be represented by the function
Applying this function to the point we have
Therefore, the resulting point is
The point $(7, 5)$ is reflected across the $x$-axis. What are the coordinates of the resulting point?
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a
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$(5,7)$ |
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b
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$(-7,5)$ |
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c
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$(5,-7)$ |
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d
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$(7,-5)$ |
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$(-5,7)$ |
The point shown above is reflected across the $y$-axis. Which of the following is the resulting point?
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When a point is reflected across the line the -coordinate and -coordinate are swapped. This transformation can be represented by the function
For example, reflecting the point in the line gives the point as shown below:
When a point is reflected in the line , the -coordinate and -coordinate swap and are transformed into their opposites (their signs are changed). This transformation can be represented by the function
For example, reflecting the point in the line gives the point as shown below:
The point is reflected across the line What are the coordinates of the resulting point?
The reflection across the line is represented by the function
Applying this function to the point we have
Therefore, the resulting point is
The point $(0,-8)$ is reflected across the line $y=-x.$ What are the coordinates of the resulting point?
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$(0,8)$ |
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b
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$(-8,8)$ |
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c
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$(0,-8)$ |
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d
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$(-8,0)$ |
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e
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$(8,0)$ |
The point shown above is reflected across the line $y=-x.$ Which of the following shows the resulting point?
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The segment shown below is reflected across the -axis. Draw the resulting segment.
To reflect a segment across a line, we
reflect the endpoints of the segment, and then
draw the segment connecting the reflected endpoints.
Reflection across the -axis can be represented by the function
Therefore, our two endpoints and are mapped to the following points by the reflection:
Therefore, reflecting our segment across the -axis, we obtain the following result:
The line segment shown above is reflected across the line $y=-x.$ Which of the following is the resulting segment?
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The segment shown above is reflected across the $x$-axis. Which of the following is the resulting segment?
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The triangle shown below is reflected across the -axis. Draw the resulting triangle.
To reflect a polygon across a line we
reflect the vertices of the polygon, and then
draw the edges connecting the reflected vertices.
Therefore, reflecting our polygon across the -axis, we obtain the following result:
A reflection maps the triangle $\mathcal T$ to the triangle $\mathcal T'$ as shown above. What is the functional representation of this transformation in the Cartesian plane?
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$f(x,y) = (x,-y)$ |
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b
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$f(x,y) = (-y,-x)$ |
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c
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$f(x,y) = (-x,y)$ |
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d
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$f(x,y) = (y,x)$ |
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e
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$f(x,y) = (-x,-y)$ |
The rectangle shown above is reflected across the $y$-axis. Which of the following is the resulting rectangle?
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