Question

write the coordinates of the vertices after a rotation 90° counterclockwise around the origin.

Explanation:

Step1: Recall the rotation rule

The rule for a \(90^{\circ}\) counter - clockwise rotation around the origin is \((x,y)\to(-y,x)\).

Step2: Find the coordinates of \(L\)

The coordinates of \(L\) are \((8,2)\). Using the rule \((x,y)\to(-y,x)\), we substitute \(x = 8\) and \(y=2\). So \(L'\) has coordinates \((-2,8)\).

Step3: Find the coordinates of \(M\)

The coordinates of \(M\) are \((8,9)\). Using the rule \((x,y)\to(-y,x)\), we substitute \(x = 8\) and \(y = 9\). So \(M'\) has coordinates \((-9,8)\).

Step4: Find the coordinates of \(N\)

The coordinates of \(N\) are \((6,0)\). Using the rule \((x,y)\to(-y,x)\), we substitute \(x = 6\) and \(y = 0\). So \(N'\) has coordinates \((0,6)\).

Answer:

\(L'(-2,8)\), \(M'(-9,8)\), \(N'(0,6)\)