Question

rotate the figure 270° clockwise around (4, 1). a(6, 8) b(10, 9) c(9, 3)

Explanation:

Step1: Translate points relative to center

Subtract the coordinates of the center of rotation $(4,1)$ from the original points.
For point $A(6,8)$: $(6 - 4,8 - 1)=(2,7)$
For point $B(10,9)$: $(10 - 4,9 - 1)=(6,8)$
For point $C(9,3)$: $(9 - 4,3 - 1)=(5,2)$

Step2: Apply 270 - degree clockwise rotation rule

The rule for a 270 - degree clockwise rotation of a point $(x,y)$ is $(y,-x)$.
For $(2,7)$: $(7,-2)$
For $(6,8)$: $(8,-6)$
For $(5,2)$: $(2,-5)$

Step3: Translate points back

Add the coordinates of the center of rotation $(4,1)$ to the rotated - relative points.
For $(7,-2)$: $(7 + 4,-2+1)=(11,-1)$
For $(8,-6)$: $(8 + 4,-6 + 1)=(12,-5)$
For $(2,-5)$: $(2 + 4,-5 + 1)=(6,-4)$

Answer:

$A'(11,-1)$
$B'(12,-5)$
$C'(6,-4)$