Question

what is the image of ( a(5,2) ) under ( r_{90^{circ}} )?

1. ( (-5,2) )
2. ( (5,-2) )
3. ( (2,5) )
4. ( (-2,5) )

Explanation:

Step1: Recall the rotation formula

When a point \((x,y)\) is rotated \(90^{\circ}\) counter - clockwise about the origin, the transformation rule is \((x,y)\to(-y,x)\).

Step2: Apply the formula to the given point

For the point \(A(5,2)\), where \(x = 5\) and \(y=2\). Substitute \(x\) and \(y\) into the formula \((x,y)\to(-y,x)\). We get \((-2,5)\).

Answer:

1. \((-2,5)\)