Question

what are the coordinates of the image ( r_{(270^{circ}, o)}(-4,5) )?
(a) ( (5,-4) )
(b) ( (-5,4) )
(c) ( (5,4) )
(d) ( (-5,-4) )

Explanation:

Step1: Recall the rotation rule

When rotating a point \((x,y)\) \(270^{\circ}\) counter - clockwise about the origin \(O\), the rule is \((x,y)\to(y, - x)\).

Step2: Apply the rule to the given point

Given the point \((-4,5)\), here \(x=-4\) and \(y = 5\).
Substitute \(x\) and \(y\) into the rule:
The new \(x\) - coordinate of the image is \(y = 5\), and the new \(y\) - coordinate of the image is \(-x=-(-4)=4\).

Answer:

A. \((5, - 4)\)