Question

question
what is the image of the point $(3,-6)$ after a rotation of $180^{circ}$ counterclockwise about the origin?
answer attempt 1 out of 2

Explanation:

Step1: Recall the rotation rule

When a point \((x,y)\) is rotated \(180^{\circ}\) counter - clockwise about the origin, the rule is \((x,y)\to(-x,-y)\).

Step2: Apply the rule to the given point

For the point \((3,-6)\), \(x = 3\) and \(y=-6\).
Using the rule \((x,y)\to(-x,-y)\), we substitute \(x = 3\) and \(y=-6\) into \(-x\) and \(-y\).
We get \(-x=-3\) and \(-y=-(-6) = 6\).

Answer:

\((-3,6)\)