Question

Triangle STU is rotated 270° counterclockwise about the origin to create triangle S’T’U’. If point U of triangle STU is (a, b), which algebraic representation best describes point U’ of triangle S’T’U’?

A) (a – 270, b – 270)
B) (a, –b)
C) (b, a)
D) (b, –a)

Answer 1

When a point (a, b) is rotated 270° counterclockwise about the origin, the new coordinates become (b, -a), so the correct algebraic representation is D) (b, -a).

Step-by-step explanation:

The question asks for the algebraic representation of a point after a triangle is rotated 270° counterclockwise about the origin. When we rotate a point (a, b) 270° counterclockwise, the new coordinates become (b, -a). This is because a 270° counterclockwise rotation is equivalent to a 90° clockwise rotation, which switches the x and y coordinates and changes the sign of the new x-coordinate.

Therefore, the correct answer is D) (b, -a).