Question

Write a rule to describe each transformation. Fill in the rest of the notation below:

U(3, -3), V(4, -1), W(5.-5)
to
V'(-1, 4), W'(-5, 5), U'(-3, 3)
(AUVW)
1. y=-
2. x-axis
3. y-axis
4. y=x

Answer 1

The correct answer is option 4. y=x. The transformation rule that describes the change from the original points to their primed counterparts is a reflection across the line y=x.

Step-by-step explanation:

This transformation rule describes a reflection across the line y=x. When we analyze the given coordinates and their transformed versions (U(3, -3) to U'(-3, 3), V(4, -1) to V'(-1, 4), and W(5,-5) to W'(-5, 5)), we see that for each point, the x-coordinate has become the y-coordinate and the y-coordinate has become the x-coordinate in the transformed point.
This switch of coordinates is characteristic of a reflection over the line y=x, which is option 4. This is because the line y=x acts as a mirror, with each point being reflected to a position where its x and y values are swapped.

transformation that reflects a point across the y-axis is called a y-axis reflection. This means that every point (x, y) is transformed to (-x, y), where the x-coordinate is negated while the y-coordinate remains the same. In this case, the points U(3, -3), V(4, -1), and W(5, -5) are transformed to U'(-3, 3), V'(-4, -1), and W'(-5, -5) respectively.

Another way to represent the y-axis reflection is by using the matrix notation. The transformation matrix for a y-axis reflection is:

[ -1 0 ]

The first column of the matrix represents the x-coordinate transformation, which in this case is negation (-1), and the second column represents the y-coordinate transformation, which remains unchanged (0).