Question

if ( p=(6,1) ), find the image of ( p ) under the following rotation.
( 180^{circ} ) counterclockwise about the origin
( (-6, square) )
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 transformation rule is \((x,y)\to(-x,-y)\).

Step2: Apply the rule to the given point

Given \(P=(6,1)\), here \(x = 6\) and \(y=1\). After rotation, \(x\) becomes \(-x=-6\) and \(y\) becomes \(-y\). Since \(y = 1\), \(-y=-1\).

Answer:

\(-1\)