describe the single transformation that would be equivalent to a reflection over the y-axis followed by a reflection over the x-axis
Just did it when you were Tommy
http://www.jiskha.com/display.cgi?id=1455143548
Basically, the prime "shape" is now diagonal from the starting shape.
| |
V | <--- .
__________________|___________________
| ^
. --->| |
|
Sorry about that weird graph-chart, it (apparently) was rejected by the website... ?
To understand the single transformation equivalent to a reflection over the y-axis followed by a reflection over the x-axis, we need to think about the effect of each reflection individually.
First, a reflection over the y-axis means that every point on the coordinate plane is mirrored across the y-axis. Points to the right of the y-axis will move to the left, while points to the left of the y-axis will move to the right. The x-coordinate of each point is negated, while the y-coordinate remains the same.
Next, a reflection over the x-axis means that every point on the coordinate plane is mirrored across the x-axis. Points above the x-axis will move below the x-axis, and points below the x-axis will move above it. The y-coordinate of each point is negated, while the x-coordinate remains the same.
To perform the equivalent single transformation, we can combine these two reflections into one step. This can be achieved by translating each point's individual transformation into a single transformation.
When a point P(x, y) is reflected over the y-axis, its coordinates change to (-x, y). Then, when this new point (-x, y) is reflected over the x-axis, its coordinates change to (-x, -y).
Therefore, the equivalent single transformation that would result from a reflection over the y-axis followed by a reflection over the x-axis is a reflection about the point (-x, -y).