Question

Finish the Rotation Notation for the following rotation:

S(0, -3), T(1, 0), U(3, -1)
to
S'(0, 3), T'(-1, 0), U'(-3, 1)
Ro_(ASTU)
1 .180
2. 90
3. 270

Answer 1

The points after rotation have coordinates inverted and multiplied by -1, indicating a 180-degree rotation about the origin. so, option 1 is the correct answer.

Step-by-step explanation:

The solution involves analyzing the rotation of points in a plane. We notice that each point (S, T, U) after rotation (S', T', U') has their coordinates inverted and multiplied by -1. This transformation is indicative of a 180-degree rotation about the origin. In this rotation, the x-coordinate becomes -x, and the y-coordinate becomes -y, which matches the change from (0, -3) to (0, 3), for example.

When rotating a point (x, y) counterclockwise by an angle θ, the coordinates of the new point (x', y') can be expressed using the rotation notation:

x' = x cos(θ) + y sin(θ)

y' = -x sin(θ) + y cos(θ)

Using the given coordinates:

S(0, -3), T(1, 0), U(3, -1)

We can apply these formulas to find the coordinates of S', T', and U':

S'(0, 3), T'(-1, 0), U'(-3, 1)