Question

question 6 of 10
abcd is rotated counterclockwise about the origin. by how many degrees was abcd rotated?
image of coordinate grid with blue square (abcd) and red square (abcd)
options: a. 360°...

Explanation:

Answer:

To determine the rotation angle, we analyze the coordinates of the original square \(ABCD\) and its image \(A'B'C'D'\) after counterclockwise rotation about the origin.

• Original Square \(ABCD\): Assume vertices (e.g., from the grid) are in the first quadrant (e.g., \(A(1,0)\), \(B(1,4)\), \(C(5,4)\), \(D(5,0)\) – approximate based on grid).
• Image \(A'B'C'D'\): After rotation, vertices lie in the second quadrant (e.g., \(A'(-1,0)\), \(B'(-5,0)\), \(C'(-5,4)\), \(D'(-1,4)\) – approximate).

A counterclockwise rotation of \(90^\circ\) about the origin transforms a point \((x,y)\) to \((-y,x)\). For a square, a \(90^\circ\) counterclockwise rotation aligns its sides perpendicular to the original (e.g., horizontal sides become vertical, or vice versa).

By comparing the orientation (original horizontal base, image vertical/horizontal in second quadrant) and using rotation rules, the rotation angle is \(90^\circ\) (assuming the full options include \(90^\circ\); if the visible option was cut off, the correct angle for a square rotated counterclockwise to move from first to second quadrant is \(90^\circ\)).

(Note: If the intended answer from the options is \(90^\circ\) (e.g., option B or similar), the final answer is \(90^\circ\).)

\(\boldsymbol{90^\circ}\)