Question

missys rotation maps point \\(k(17, -12)\\) to \\(k(12, 17)\\). which describes the rotation?

\\(270^\circ\\) counterclockwise rotation
\\(90^\circ\\) counterclockwise rotation
\\(90^\circ\\) clockwise rotation
\\(180^\circ\\) rotation

Explanation:

Identify coordinates

We are given the original point \(K(17, -12)\) and its image \(K'(12, 17)\) after a rotation about the origin. Let the coordinates of \(K\) be \((x, y) = (17, -12)\).

Analyze transformation

Using the Rotation Rules concept, we compare the coordinates of \(K(x, y)\) and \(K'(x', y')\):

• \(x = 17\)
• \(y = -12\)
• \(x' = 12 = -y\)
• \(y' = 17 = x\)

Thus, the mapping is \((x, y)
ightarrow (-y, x)\).

Determine rotation

Using the Rotation Rules concept, we identify the standard coordinate transformation rules about the origin:

• A \(90^\circ\) counterclockwise rotation maps \((x, y)

ightarrow (-y, x)\).

• A \(90^\circ\) clockwise rotation maps \((x, y)

ightarrow (y, -x)\).

• A \(180^\circ\) rotation maps \((x, y)

ightarrow (-x, -y)\).

• A \(270^\circ\) counterclockwise rotation maps \((x, y)

ightarrow (y, -x)\).

Since our mapping is \((x, y)
ightarrow (-y, x)\), this represents a \(90^\circ\) counterclockwise rotation.

Answer:

• (A) \(270^\circ\) counterclockwise rotation
• (B) \(90^\circ\) counterclockwise rotation (Correct answer)
• (C) \(90^\circ\) clockwise rotation
• (D) \(180^\circ\) rotation