Question

rotate △stu 90° clockwise around the origin.

Explanation:

Step1: Find the coordinates of the original points

Assume the coordinates of \(S\), \(T\), \(U\) are \(S(-2, - 4)\), \(T(-1,-7)\), \(U(-4,-7)\) (based on the grid - like graph structure).

Step2: Apply the \(90^{\circ}\) clockwise rotation formula

The formula for a \(90^{\circ}\) clockwise rotation about the origin \((x,y)\to(y, - x)\).
For point \(S(-2,-4)\):
Substitute \(x=-2\) and \(y = - 4\) into the formula \((x,y)\to(y,-x)\), we get \(S'(-4,2)\).
For point \(T(-1,-7)\):
Substitute \(x=-1\) and \(y=-7\) into the formula \((x,y)\to(y,-x)\), we get \(T'(-7,1)\).
For point \(U(-4,-7)\):
Substitute \(x = - 4\) and \(y=-7\) into the formula \((x,y)\to(y,-x)\), we get \(U'(-7,4)\).

Answer:

The coordinates of the vertices of the rotated triangle \(\triangle S'T'U'\) are \(S'(-4,2)\), \(T'(-7,1)\), \(U'(-7,4)\)