Which shows the image of quadrilateral ABCD after the transformation R0, 90°?

Question

On a coordinate plane, a rectangle has points A (negative 1, 0), B (0, negative 1), C (negative 2, negative 3), D (negative 3, negative 2).

On a coordinate plane, a rectangle has points A prime (0, negative 1), B prime (1, 0), C prime (3, negative 2), D prime (2, negative 3).
On a coordinate plane, a rectangle has points A prime (0, 1), B prime (0, negative 1), C prime (negative 3, 2), D prime (negative 2, 3).
On a coordinate plane, a rectangle has points A prime (0, negative 1), B prime (negative 1, 0), C prime (negative 3, negative 2), D prime (negative 2, negative 3).
On a coordinate plane, a rectangle has points A prime (1, 0), B prime (0, 1), C prime (2, 3), D prime (3, 2).
Mark this and return

Answer 1

To determine the image of quadrilateral ABCD after the transformation \( R_{0, 90^\circ} \) (a 90-degree rotation about the origin), we can apply the transformation to each point of the quadrilateral.

For a 90-degree rotation counterclockwise about the origin, the transformation of a point \((x, y)\) can be expressed as:

\[ (x, y) \rightarrow (-y, x) \]

Let's apply this transformation to each of the points A, B, C, and D:

• Point A (-1, 0): \[ (-1, 0) \rightarrow (0, -1) \]

• Point B (0, -1): \[ (0, -1) \rightarrow (1, 0) \]

• Point C (-2, -3): \[ (-2, -3) \rightarrow (3, -2) \]

• Point D (-3, -2): \[ (-3, -2) \rightarrow (2, -3) \]

So after the transformation, the new coordinates of the points are:

• \( A' (0, -1) \)
• \( B' (1, 0) \)
• \( C' (3, -2) \)
• \( D' (2, -3) \)

Now we can compare these points with the options provided:

1. A' (0, -1), B' (1, 0), C' (3, -2), D' (2, -3) <- This is correct.
2. A' (0, 1), B' (0, -1), C' (-3, 2), D' (-2, 3)
3. A' (0, -1), B' (-1, 0), C' (-3, -2), D' (-2, -3)
4. A' (1, 0), B' (0, 1), C' (2, 3), D' (3, 2)

The correct image of the quadrilateral ABCD after the transformation \( R_{0, 90^\circ} \) is:

A' (0, -1), B' (1, 0), C' (3, -2), D' (2, -3).