Question

1. if figure jkf is rotated 90 degrees clockwise, what quadrant will it be in?
2. if figure jkf is rotated 90 degrees counterclockwise, what quadrant will it be in?
3. if figure jkf is rotated 180 degrees clockwise, what quadrant will it be in?
4. if figure jkf is rotated 180 degrees counterclockwise, what quadrant will it be in?

Explanation:

Step1: Determine the original quadrant

The figure \(JKF\) is in the first quadrant (where \(x>0,y > 0\)).

Step2: Analyze \(90^{\circ}\) clock - wise rotation

When a point \((x,y)\) is rotated \(90^{\circ}\) clock - wise about the origin, the transformation rule is \((x,y)\to(y, - x)\). Points in the first quadrant \((x>0,y>0)\) will be mapped to the fourth quadrant (\(y>0,-x < 0\) is not correct, actually \((x,y)\to(y,-x)\), for positive \(x\) and \(y\), \(y>0\) and \(-x<0\), so the new points will be in the fourth quadrant).

Step3: Analyze \(90^{\circ}\) counter - clockwise rotation

When a point \((x,y)\) is rotated \(90^{\circ}\) counter - clockwise about the origin, the transformation rule is \((x,y)\to(-y,x)\). Points in the first quadrant \((x > 0,y>0)\) will be mapped to the second quadrant (\(-y<0,x>0\)).

Step4: Analyze \(180^{\circ}\) rotation (clockwise or counter - clockwise)

When a point \((x,y)\) is rotated \(180^{\circ}\) about the origin (clockwise or counter - clockwise, since \(180^{\circ}\) clockwise rotation \((x,y)\to(-x,-y)\) and \(180^{\circ}\) counter - clockwise rotation \((x,y)\to(-x,-y)\)), points in the first quadrant \((x>0,y>0)\) will be mapped to the third quadrant (\(-x<0,-y < 0\)).

Answer:

1. Fourth quadrant
2. Second quadrant
3. Third quadrant
4. Third quadrant