The reflection of a point ( P ) across an axis (such as the x-axis or y-axis) results in a new point ( P' ) that is equidistant from the axis but on the opposite side. For example, if ( P ) is at coordinates ( (x, y) ), its reflection across the x-axis would be ( P' ) at ( (x, -y) ). The distance between ( P ) and the axis remains the same, ensuring that the two points are symmetrical with respect to that axis.
The reflection of a point or shape across the y-axis involves changing the sign of the x-coordinates while keeping the y-coordinates the same. For example, if you have a point (x, y), its reflection across the y-axis would be (-x, y). This transformation effectively flips the figure horizontally, creating a mirror image on the opposite side of the y-axis.
In transformations a reflection across the x axis produces a mirror image
Yes, a point at (0, 4) can be reflected across the y-axis. When reflecting a point across the y-axis, the x-coordinate changes sign while the y-coordinate remains the same. Therefore, the reflection of the point (0, 4) across the y-axis is still (0, 4), as the x-coordinate is already zero.
When the point (-3, 2) is reflected across the x-axis, the y-coordinate changes sign while the x-coordinate remains the same. Thus, the resulting image of the point after the reflection is (-3, -2).
(2.5,-2.75)
Reflection across the y-axis changes the sign of the x - coordinate only, that is, (x, y) becomes (-x, y).
The reflection of a point or shape across the y-axis involves changing the sign of the x-coordinates while keeping the y-coordinates the same. For example, if you have a point (x, y), its reflection across the y-axis would be (-x, y). This transformation effectively flips the figure horizontally, creating a mirror image on the opposite side of the y-axis.
The reflection of a point across the y-axis involves changing the sign of the x-coordinate while keeping the y-coordinate the same. In this case, the point (-1, -5) will reflect to (1, -5) across the y-axis. This is because the x-coordinate changes from -1 to 1, while the y-coordinate remains -5.
In transformations a reflection across the x axis produces a mirror image
Yes, a point at (0, 4) can be reflected across the y-axis. When reflecting a point across the y-axis, the x-coordinate changes sign while the y-coordinate remains the same. Therefore, the reflection of the point (0, 4) across the y-axis is still (0, 4), as the x-coordinate is already zero.
y' = y, x' = -x.
For a reflection across the x axis, both the slope and the y intercept would have the same magnitude but the opposite sign.
y = -f(x) is a reflection of y = f(x) in the x axis.
If your points are (p,f), they become (p,-f).
Example: if you have a point with the coordinates (2,4), a reflection over the y-axis will result in the point with coordinates (-2,4).
When the point (-3, 2) is reflected across the x-axis, the y-coordinate changes sign while the x-coordinate remains the same. Thus, the resulting image of the point after the reflection is (-3, -2).
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