Question

1. rotate the coordinate (3, 5) 90° counter - clockwise around the point (1, -8)
2. rotate the coordinate (-1, 6) 270° clockwise around the point (4, -2)

Explanation:

Step1: Shift to origin (Q20)

First, translate the point so the center of rotation (1, -8) becomes the origin. Subtract the center's coordinates from the original point.
Original point: $(3, 5)$
Shifted coordinates: $(3-1, 5-(-8))=(2, 13)$

Step2: 90° counterclockwise rotate (Q20)

Use 90° counterclockwise rotation rule: $(x,y)\to(-y,x)$
Rotated shifted coordinates: $(-13, 2)$

Step3: Shift back (Q20)

Add the center of rotation's coordinates to the rotated shifted point.
Final coordinates: $(-13+1, 2+(-8))=(-12, -6)$

Step4: Shift to origin (Q21)

Translate the point so the center of rotation (4, -2) becomes the origin. Subtract the center's coordinates from the original point.
Original point: $(-1, 6)$
Shifted coordinates: $(-1-4, 6-(-2))=(-5, 8)$

Step5: 270° clockwise rotate (Q21)

270° clockwise rotation is equivalent to 90° counterclockwise, rule: $(x,y)\to(-y,x)$
Rotated shifted coordinates: $(-8, -5)$

Step6: Shift back (Q21)

Add the center of rotation's coordinates to the rotated shifted point.
Final coordinates: $(-8+4, -5+(-2))=(-4, -7)$

Answer:

1. For question 20: $(-12, -6)$
2. For question 21: $(-4, -7)$