describe the single transformation that would be equivalent to a reflection over the y-axis followed by a reflection over the x-axis
no
Reflection
To understand the single transformation that would be equivalent to a reflection over the y-axis followed by a reflection over the x-axis, let's break it down step by step:
1. Reflection over the y-axis:
When reflecting over the y-axis, each point in the coordinate plane will have its x-coordinate negated while keeping the y-coordinate the same. For example, if you have a point (2, 3), after reflecting over the y-axis, it would become (-2, 3). This essentially flips the figure or object horizontally.
2. Reflection over the x-axis:
When reflecting over the x-axis, each point in the coordinate plane will have its y-coordinate negated while keeping the x-coordinate the same. Continuing from the previous example, after reflecting over the x-axis, the point (-2, 3) would become (-2, -3). This essentially flips the figure or object vertically.
Now, to find the single transformation that combines both reflections, we need to consider what happens when we perform both of them in sequence.
If we reflect a point (x, y) over the y-axis, the x-coordinate becomes -x, and the y-coordinate stays the same: (-x, y).
Then, if we take this reflected point (-x, y) and reflect it over the x-axis, the y-coordinate becomes -y, and the x-coordinate remains the same: (-x, -y).
Therefore, the single transformation that would be equivalent to a reflection over the y-axis followed by a reflection over the x-axis is a single reflection over the point (-0, 0), which has no effect on the object or figure.
reflection in the y-axis
(x,y) ---> (-x,y)
reflection in the x-axis
(-x,y) ---> (-x, -y)
so (x,y) --> (-x,-y) , which is a reflection in the origin.
pick a point and illustrate it on a grid.
e.g. watch what happens to (3,5)