Question

c. rotate 90° clockwise around (-2,1).

Explanation:

Step1: Identify original coordinates

First, find the coordinates of the vertices (let's assume the vertices are \( A, B, C, D \)). From the grid:

• Let's assume \( A(-3, 9) \), \( B(-4, 7) \), \( C(-3, 6) \), \( D(-1, 7) \) (need to confirm from grid, but general method: subtract the center \((-2,1)\) to get relative coordinates).

Step2: Translate to center

For a point \((x,y)\), translate to \((x', y')=(x + 2, y - 1)\) (since center is \((-2,1)\), so \( x'=x - (-2)=x + 2 \), \( y'=y - 1 \)).

• For \( A(-3,9) \): \( x'=-3 + 2=-1 \), \( y'=9 - 1 = 8 \)
• For \( B(-4,7) \): \( x'=-4 + 2=-2 \), \( y'=7 - 1 = 6 \)
• For \( C(-3,6) \): \( x'=-3 + 2=-1 \), \( y'=6 - 1 = 5 \)
• For \( D(-1,7) \): \( x'=-1 + 2=1 \), \( y'=7 - 1 = 6 \)

Step3: Rotate 90° clockwise

The rule for 90° clockwise rotation of a point \((x', y')\) is \((x'', y'')=(y', -x')\).

• For \( A'(-1,8) \): \( x''=8 \), \( y''=-(-1)=1 \) → \( (8,1) \)
• For \( B'(-2,6) \): \( x''=6 \), \( y''=-(-2)=2 \) → \( (6,2) \)
• For \( C'(-1,5) \): \( x''=5 \), \( y''=-(-1)=1 \) → \( (5,1) \)
• For \( D'(1,6) \): \( x''=6 \), \( y''=-1 \) → \( (6,-1) \)

Step4: Translate back

Translate back by subtracting 2 from \( x'' \) and adding 1 to \( y'' \) (reverse of step 2: \( x = x'' - 2 \), \( y = y'' + 1 \)).

• For \( A''(8,1) \): \( x=8 - 2=6 \), \( y=1 + 1=2 \) → \( (6,2) \)
• For \( B''(6,2) \): \( x=6 - 2=4 \), \( y=2 + 1=3 \) → \( (4,3) \)
• For \( C''(5,1) \): \( x=5 - 2=3 \), \( y=1 + 1=2 \) → \( (3,2) \)
• For \( D''(6,-1) \): \( x=6 - 2=4 \), \( y=-1 + 1=0 \) → \( (4,0) \)

(Note: Coordinates may vary based on exact grid reading, but the method is translate to center, rotate, translate back.)

Answer:

The rotated vertices (example with correct method) would be calculated as above. For precise coordinates, recheck grid points, but the process is: translate to center \((-2,1)\), apply 90° clockwise rotation \((x,y)\to(y,-x)\), then translate back.