Question

rotate the figure 270° clockwise around (6, 8). d(1, 4) e(5, 5) f(4, 1)

Explanation:

Step1: Translate points relative to center

For a point $(x,y)$ rotated around $(a,b)$, first find the relative - coordinates $(x - a,y - b)$.
For point $D(1,4)$ relative to $(6,8)$: $(1 - 6,4 - 8)=(-5,-4)$.
For point $E(5,5)$ relative to $(6,8)$: $(5 - 6,5 - 8)=(-1,-3)$.
For point $F(4,1)$ relative to $(6,8)$: $(4 - 6,1 - 8)=(-2,-7)$.

Step2: Apply 270 - degree clockwise rotation rule

The rule for a 270 - degree clockwise rotation of a point $(x,y)$ is $(y,-x)$.
For $(-5,-4)$ after rotation: $(-4,5)$.
For $(-1,-3)$ after rotation: $(-3,1)$.
For $(-2,-7)$ after rotation: $(-7,2)$.

Step3: Translate back to original coordinate system

Add the center coordinates $(a,b)$ back.
For the rotated point of $D$: $(-4 + 6,5 + 8)=(2,13)$.
For the rotated point of $E$: $(-3+6,1 + 8)=(3,9)$.
For the rotated point of $F$: $(-7 + 6,2 + 8)=(-1,10)$.

Answer:

$D'(2,13)$
$E'(3,9)$
$F'(-1,10)$