Question

What are the three vertices of the triangle if it is rotated about the origin 90° counterclockwise?

A. (-1, -4), (1, 4), (-4, -2)
B. (4, 2), (2, -1), (-1, -4)
C. (1, 4), (-4, -2), (2, -1)
D. (-4, -2), (2, -1), (1, 4)

Answer 1

After applying a 90° counterclockwise rotation transformation to the vertices of a triangle, option B is the only one that correctly reflects the resultant vertices of the triangle.

Step-by-step explanation:

To find the new vertices of a triangle after a 90° counterclockwise rotation about the origin, we apply the rotation transformation rules for each vertex. The general rule for a 90° counterclockwise rotation of a point (x, y) is to transform it to (-y, x). Let's apply this rule to the provided options:

• A. (-1, -4) becomes (4, -1), (1, 4) becomes (-4, 1), (-4, -2) becomes (2, -4)
• B. (4, 2) becomes (-2, 4), (2, -1) becomes (1, 2), (-1, -4) becomes (4, -1)
• C. (1, 4) becomes (-4, 1), (-4, -2) becomes (2, -4), (2, -1) becomes (1, 2)
• D. (-4, -2) becomes (2, -4), (2, -1) becomes (1, 2), (1, 4) becomes (-4, 1)

From the above, only option B correctly reflects the vertices after the described rotation.