Question

if p = (6,1), find the image of p under the following rotation. 180° counterclockwise about the origin (?, ) enter the number that belongs in the green box.

Explanation:

Step1: Recall the rotation rule

When a point \((x,y)\) is rotated \(180^{\circ}\) counter - clockwise about the origin, the new coordinates \((x',y')\) are given by \((x',y')=(-x,-y)\).

Step2: Apply the rule to the given point

For the point \(P=(6,1)\), where \(x = 6\) and \(y = 1\). After rotation, the \(x\) - coordinate of the image is \(x'=-6\) and the \(y\) - coordinate is \(y'=-1\).

Answer:

\(-6\)