Question

write the coordinates of the vertices after a rotation 90° counterclockwise

Explanation:

Step1: Recall the rotation rule

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

Step2: Find the coordinates of the original vertices

From the graph, the coordinates of \(J\) are \((-8,3)\), the coordinates of \(K\) are \((-8,9)\), and the coordinates of \(L\) are \((-2,0)\).

Step3: Apply the rotation rule to each vertex

For \(J(-8,3)\):
Substitute \(x = - 8\) and \(y = 3\) into the rule \((x,y)\to(-y,x)\).
We get \(J'(-3,-8)\).
For \(K(-8,9)\):
Substitute \(x=-8\) and \(y = 9\) into the rule \((x,y)\to(-y,x)\).
We get \(K'(-9,-8)\).
For \(L(-2,0)\):
Substitute \(x=-2\) and \(y = 0\) into the rule \((x,y)\to(-y,x)\).
We get \(L'(0,-2)\).

Answer:

The coordinates of \(J'\) are \((-3,-8)\), the coordinates of \(K'\) are \((-9,-8)\) and the coordinates of \(L'\) are \((0,-2)\)