Question

What are the coordinates of each vertex if the figure is rotated 90° counterclockwise about the origin?

A. A'(-2, 2), B'(-5. - 2). C'(-3, -6),D (3,-4)

B. A' (2, – 2), B' (5,2), C'(3,6). D(-3,4)

C. A'(-2, – 2),B'(-5,2),C'(-3, 6),D(3,4)

D. A'(2, 2), B'(5,- 2),C'(3,-6),D'(-3,-4)

Answer 1

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Explanation:

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Answer 2

The correct answer is option A.) A′(-1, 4),B′(-4, -1),C′(1, -4),D′ (4, 1).

Rotating a square 90° counterclockwise about the origin can be visualized as pivoting one corner around the origin until it occupies the adjacent corner's position. This motion essentially swaps the positions of diagonally opposite corners while also flipping them across the x and y axes. Consequently, the signs of their respective coordinates are negated.

To determine the new coordinates of each vertex after the rotation, we can rewrite the original coordinates as (x, y) and apply the following transformation rule:

• Swap the x and y coordinates: (y, x).
• Negate both coordinates: (-y, -x).

Let's apply this rule to the original square's vertices:

• A (4, 1) becomes (-1, 4).
• B (1, -4) becomes (-4, -1).
• C (-4, -1) becomes (1, -4).
• D (-1, 4) becomes (4, 1).

Therefore, after a 90° counterclockwise rotation, the square's vertices will be located at:

• A' (-1, 4)
• B' (-4, -1)
• C' (1, -4)
• D' (4, 1)

This confirms that option A.) A′(-1, 4),B′(-4, -1),C′(1, -4),D′ (4, 1) is the correct answer.