Question

rotate the figure 90° clockwise around (-1, -4). p(0, -6) q(5, -4) r(4, -7)

Explanation:

Step1: Translate points

First, translate the rotation - center and the points so that the rotation - center is at the origin. Let the rotation - center $C(-1,-4)$. For point $P(0, - 6)$, the translated point $P_1=(0 - (-1),-6-(-4))=(1, - 2)$. For point $Q(5,-4)$, the translated point $Q_1=(5 - (-1),-4-(-4))=(6,0)$. For point $R(4,-7)$, the translated point $R_1=(4 - (-1),-7-(-4))=(5,-3)$.

Step2: Apply 90 - degree clockwise rotation formula

The formula for a 90 - degree clockwise rotation of a point $(x,y)$ about the origin is $(y,-x)$. For $P_1(1,-2)$, the rotated point $P_2=(-2,-1)$. For $Q_1(6,0)$, the rotated point $Q_2=(0,-6)$. For $R_1(5,-3)$, the rotated point $R_2=(-3,-5)$.

Step3: Translate back

Translate the rotated points back to the original coordinate system. For $P_2(-2,-1)$, the final point $P'=(-2+(-1),-1+(-4))=(-3,-5)$. For $Q_2(0,-6)$, the final point $Q'=(0+(-1),-6+(-4))=(-1,-10)$. For $R_2(-3,-5)$, the final point $R'=(-3+(-1),-5+(-4))=(-4,-9)$.

Answer:

$P'(-3,-5)$
$Q'(-1,-10)$
$R'(-4,-9)$