Question

Write the coordinates of the vertices after a rotation 270 clockwise around the origin Q(-9,1) R(0,1) S(0,10) T (-9,10).

A. Q'(1,9) R(1,0) S(10,0) T(10,9)
B. Q'(1,-9) R(-1,0) S(0,-10) T(-10,-9)
C. Q'(9,-1) R(0,-1) S(0,-10) T(9,-10)
D. Q'(-1,9) R(0,1) S(10,0) T(10,-9)

Answer 1

The coordinates of the vertices Q, R, S, and T after a 270-degree clockwise rotation around the origin are Q'(9, -1), R'(1, 0), S'(0, -10), and T'(9, -10).

Step-by-step explanation:

The question asks for the coordinates of the vertices after a 270 degree clockwise rotation around the origin of the points Q(-9, 1), R(0, 1), S(0, 10), and T(-9, 10). When performing a clockwise rotation of 270 degrees (which is equivalent to a 90-degree counterclockwise rotation) around the origin, we can use the transformation rules for rotation in the Cartesian coordinate system. These rules state that for a point (x, y) after a 90-degree counterclockwise rotation, the new coordinates will be (-y, x). Therefore, applying this transformation to each point:

• For Q(-9, 1), Q' will be (-1, -9).
• For R(0, 1), R' will be (-1, 0).
• For S(0, 10), S' will be (-10, 0).
• For T(-9, 10), T' will be (-10, -9).

The correct set of coordinates after the 270-degree clockwise rotation is therefore C. Q'(9, -1), R'(1, 0), S'(0, -10), and T'(9, -10).