Question

rotate △jkl 90° counterclockwise around the origin.

Explanation:

Step1: Find the coordinates of \(J\), \(K\), \(L\)

Assume \(J=(2, - 2)\), \(K=(6,-2)\), \(L=(2,-6)\) (based on the grid - like structure in the coordinate plane).
The rule for a \(90^{\circ}\) counter - clockwise rotation about the origin \((x,y)\to(-y,x)\).

Step2: Apply the rotation rule to each point

For point \(J=(2,-2)\):
Substitute \(x = 2\) and \(y=-2\) into the rule \((x,y)\to(-y,x)\).
We get \(J'=(2,2)\) (since \(-y=-(-2) = 2\) and \(x = 2\)).
For point \(K=(6,-2)\):
Substitute \(x = 6\) and \(y=-2\) into the rule \((x,y)\to(-y,x)\).
We get \(K'=(2,6)\) (since \(-y=-(-2)=2\) and \(x = 6\)).
For point \(L=(2,-6)\):
Substitute \(x = 2\) and \(y=-6\) into the rule \((x,y)\to(-y,x)\).
We get \(L'=(6,2)\) (since \(-y=-(-6)=6\) and \(x = 2\)).

Answer:

The coordinates of the rotated triangle \(\triangle J'K'L'\) are \(J'(2,2)\), \(K'(2,6)\), \(L'(6,2)\)