Question

after rotating point ( d(6,-2) 90^{circ} ) counterclockwise about the origin, which are the coordinates of the new point?
( (2,6) )
( (6,2) )
( (-6,2) )
( (-2,-6) )

Explanation:

Step1: Recall the rotation rule

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

Step2: Apply the rule to the given point

For the point \(D(6,-2)\), here \(x = 6\) and \(y=-2\).
Using the rule \((x,y)\to(-y,x)\), we substitute \(y=-2\) and \(x = 6\).
We get \(x'=-(-2)=2\) and \(y'=6\).

Answer:

\((2,6)\)