Question

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

Explanation:

Step1: Recall the rotation rule

When a point \((x,y)\) is rotated \(90^{\circ}\) counter - clockwise around the origin, the new coordinates \((x',y')\) follow the rule \((x,y)\to(-y,x)\).

Step2: Find the coordinates of the original points

From the graph, \(S(-7,1)\), \(T(-7,10)\), \(U(-2,10)\), \(V(-2,1)\).

Step3: Apply the rotation rule to each point

For point \(S(-7,1)\):
Using the rule \((x,y)\to(-y,x)\), substitute \(x = - 7\) and \(y = 1\).
\(x'=-1\), \(y'=-7\), so \(S'(-1,-7)\).
For point \(T(-7,10)\):
Substitute \(x=-7\) and \(y = 10\) into \((x,y)\to(-y,x)\).
\(x'=-10\), \(y'=-7\), so \(T'(-10,-7)\).
For point \(U(-2,10)\):
Substitute \(x=-2\) and \(y = 10\) into \((x,y)\to(-y,x)\).
\(x'=-10\), \(y'=-2\), so \(U'(-10,-2)\).
For point \(V(-2,1)\):
Substitute \(x=-2\) and \(y = 1\) into \((x,y)\to(-y,x)\).
\(x'=-1\), \(y'=-2\), so \(V'(-1,-2)\).

Answer:

\(S'(-1,-7)\), \(T'(-10,-7)\), \(U'(-10,-2)\), \(V'(-1,-2)\)