I only need to answer the first one, but I need you to tell me if the others are correct or incorrect, if they are incorrect please help me. Rotation of 90 degrees counter clockwise of point A (7, 4).
Quadrant of given point: 1
Coordinates after the switch: 4, 7
Quadrant after rotation:
New coordinates after rotation:

Rotation of 180 degrees of point B at (-8, -2).
Quadrant of given point: 3
Quadrant after rotation: 1
New coordinates after rotation: 8, 2

Rotation of 270 degrees clockwise around the origin of point C at (9, -5).
Quadrant of given point: 4
Coordinates after the switch: 5, 9
Quadrant after rotation: 1
New coordinates after rotation: 5. 9

Rotation of 90 degrees clockwise around the origin of point D at (-6, -11).
Quadrant of given point: 3
Coordinates after the switch: 11, 6
Quadrant after the rotation: 2
New coordinates after rotation: -11, 6

9514 1404 393

  A'(-4, 7) . . . . ending in quadrant 2

  check switched coordinates for C', D'

Step-by-step explanation:

The transformations accomplished by rotations are ...

  (x, y) ⇒ (-y, x) . . . . . 90° CCW or 270° CW

  (x, y) ⇒ (y, -x) . . . . . 90° CW or 270° CCW

  (x, y) ⇒ (-x, -y) . . . .  180° (either direction)

You notice that coordinates are switched and one is negated in each of these transformations. I assume that your line "Coordinates after the switch" is intended to lead you through that first step, then "New coordinates after rotation" is intended to be the same set of coordinates with the appropriate sign change.

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1. A(7, 4) 90° CCW ⇒ (4, 7) ⇒ A'(-4, 7) . . . . ending in quadrant 2

2. B(-8, -1) 180° ⇒ B'(8, 2) . . . . ending in quadrant 1 (correct)

3. C(9, -5) 270° CW ⇒ (-5, 9)* ⇒ C'(5, 9) . . . . ending in quadrant 1

4. D(-6, -11) 90° CW ⇒ (-11, -6)* ⇒ D'(-11, 6) . . . . ending in quadrant 2

* I would leave the original signs on the "coordinates after the switch". Here, you have dropped the signs. I don't know what you've been taught, but that's not how I would do it, as you can see above.

b

step-by-step explanation:

2nd one in the first row is correct