Question

write the coordinates of the vertices after a rotation 180° counterclockwise around the origin.

Explanation:

Step1: Identify original coordinates

The original coordinates of the vertices are \(Q(6,2)\), \(T(8,2)\), \(S(8,8)\), \(R(6,8)\).

Step2: Apply 180 - degree rotation rule

The rule for a 180 - degree counter - clockwise rotation around the origin is \((x,y)\to(-x,-y)\).
For point \(Q(6,2)\), after rotation, the new coordinates are \(Q'(-6,-2)\).
For point \(T(8,2)\), after rotation, the new coordinates are \(T'(-8,-2)\).
For point \(S(8,8)\), after rotation, the new coordinates are \(S'(-8,-8)\).
For point \(R(6,8)\), after rotation, the new coordinates are \(R'(-6,-8)\).

Answer:

The new coordinates of the vertices are \(Q'(-6,-2)\), \(T'(-8,-2)\), \(S'(-8,-8)\), \(R'(-6,-8)\)