One vertex of a polygon is located at (3, –2). after a rotation, the vertex is located at (2, 3). which transformations could have taken place? check all that apply.
r0, 90°
r0, 180°
r0, 270°
r0, –90°
r0, –270°

The vertex has a rotation (3,-2) --> (2,3).
Or in x and y coordinates, (x,y) --> (-y,x).
The rotation that has this said rule is R0, 90°. And 90° is equal to –270°. 
The answers are:
R0, 90°
R0, –270°.

Additional information:
R0, 180° has the rule (x, y) → (-x, -y)
R0, 270° and R0, –90° has the rule  (x, y) → (y, -x).

R(O, 90°)R(O, –270°)Further explanation

Given:

One vertex of a polygon with the following conditions.

Before rotation about the origin is located at (3, -2)After rotation about the origin is located at (2, 3)

Question:

Which transformations could have taken place?

The Process:

This condition fulfills two types of rotation, namely:

Notes:

We already know there are four types of transformation geometry: Translation, Reflection, Rotation, and Dilation. In this case, we only focus on rotation.

Rotation represents a type of transformation in which a figure is rotated about fixed points called centers of rotation.  The result of rotation is the same shape and size, but the figures may be turned in different directions.  Rotations may be clockwise or counterclockwise. A positive angle of rotation moves the figure counterclockwise, and a negative angle turns the figure clockwise.

However, we must moreover know about the use of multiplier matrices in transformation geometry.

For example, the matrix used in rotation 90° in the counterclockwise direction is

State (x, y) as the initial coordinate and (x', y') as the final coordinate.

The results of rotation are obtained from the multiplication of the matrix with the initial coordinates.  

Remember that if a point is rotated 90 ° about the origin, then it is the same as the point rotated -270 ° about the origin.

Based on the results of the matrix operation, the rule that describes the rotation with some special angles about the origin is as follows.

Learn moreWhat transformations change the graph of (f)x to the graph of g(x)? The problem of shifting A triangle is rotated 90° about the origin

Keywords: one vertex of a polygon, after rotation, angle, about the origin, transformation, the rule, matrix operation, cos, sin, 90°, -90°, 270°, -270°, 180°, -180°, (x, y), which transformations could have taken place?

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