Question

clue 9
point k (1, 5) was rotated to point k (5, -1). how many degrees was point k rotated?
360° the murder did not happen in the parlor.
270° the murder did not happen in the guest house.
180° the murder did not happen in the library.
90° the murder did not happen in the corridor.

Explanation:

Step1: Recall rotation rules

When a point \((x,y)\) is rotated \(90^{\circ}\) clockwise about the origin, the new coordinates \((x',y')\) are given by the transformation \((x,y)\to(y,-x)\).
For point \(K(1,5)\), if we apply the \(90^{\circ}\) clockwise rotation rule:
Substitute \(x = 1\) and \(y=5\) into \((y,-x)\).
We get \(x'=5\) and \(y'=- 1\), which is the point \(K'(5,-1)\)

Answer:

\(90^{\circ}\)