Question

10.) rotate 180° cw
11.) rotate 90° cw
12.) rotate 90° ccw

Explanation:

Problem 10: Rotate 180° CW

Step 1: Recall 180° rotation rule

For a point \((x,y)\), rotating 180° (clockwise or counterclockwise) gives \((-x,-y)\).

Step 2: Identify coordinates (assume grid units)

Let's assume the coordinates:

• \(A\): Let's say \(A = (-1, 3)\) (from grid, left of y - axis, above x - axis)
• \(B = (-1, 1)\)
• \(C = (-4, 1)\)
• \(D = (-4, 3)\)

Step 3: Apply 180° rotation

• For \(A(-1,3)\): New \(A'=(1, - 3)\)
• For \(B(-1,1)\): New \(B'=(1, - 1)\)
• For \(C(-4,1)\): New \(C'=(4, - 1)\)
• For \(D(-4,3)\): New \(D'=(4, - 3)\)

Step 4: Plot the new points

Plot \(A'(1,-3)\), \(B'(1,-1)\), \(C'(4,-1)\), \(D'(4,-3)\) and connect them to get the rotated figure.

Problem 11: Rotate 90° CW

Step 1: Recall 90° CW rotation rule

For a point \((x,y)\), rotating 90° clockwise gives \((y,-x)\).

Step 2: Identify coordinates (assume grid units)

Let's assume the coordinates:

• \(A=(3, 3)\)
• \(B=(3, 1)\)
• \(C=(2, 1)\)
• \(D=(2, 3)\)

Step 3: Apply 90° CW rotation

• For \(A(3,3)\): New \(A'=(3,-3)\)
• For \(B(3,1)\): New \(B'=(1,-3)\)
• For \(C(2,1)\): New \(C'=(1,-2)\)
• For \(D(2,3)\): New \(D'=(3,-2)\)

Step 4: Plot the new points

Plot \(A'(3,-3)\), \(B'(1,-3)\), \(C'(1,-2)\), \(D'(3,-2)\) and connect them to get the rotated figure.

Problem 12: Rotate 90° CCW

Step 1: Recall 90° CCW rotation rule

For a point \((x,y)\), rotating 90° counter - clockwise gives \((-y,x)\).

Step 2: Identify coordinates (assume grid units)

Let's assume the coordinates:

• \(A=(4, 2)\)
• \(B=(2, 1)\)
• \(C=(1, 3)\)

Step 3: Apply 90° CCW rotation

• For \(A(4,2)\): New \(A'=(-2,4)\)
• For \(B(2,1)\): New \(B'=(-1,2)\)
• For \(C(1,3)\): New \(C'=(-3,1)\)

Step 4: Plot the new points

Plot \(A'(-2,4)\), \(B'(-1,2)\), \(C'(-3,1)\) and connect them to get the rotated figure.

Answer:

s:

• Problem 10: The figure after 180° CW rotation has vertices at \((1,-3)\), \((1,-1)\), \((4,-1)\), \((4,-3)\) (plotted in the fourth quadrant relative to the original).
• Problem 11: The figure after 90° CW rotation has vertices at \((3,-3)\), \((1,-3)\), \((1,-2)\), \((3,-2)\) (plotted in the fourth quadrant relative to the original).
• Problem 12: The figure after 90° CCW rotation has vertices at \((-2,4)\), \((-1,2)\), \((-3,1)\) (plotted in the second quadrant relative to the original).

(Note: The actual coordinates may vary slightly depending on the exact grid placement, but the method of applying the rotation rules is consistent.)