Question

3.3b hw honors
rotate the figure 90° clockwise around (-5, -4). a(-13, -3) b(-7, 3) c(-6, -2)

Explanation:

Step1: Recall rotation formula

The formula for a 90 - degree clock - wise rotation around a point $(h,k)$ is $(x,y)\to(h+(y - k),k-(x - h))$.

Step2: Rotate point A

For point $A(-13,-3)$ with $(h,k)=(-5,-4)$:
$x=-13,y = - 3$.
$x_{new}=-5+(-3+4)=-5 + 1=-4$.
$y_{new}=-4-(-13 + 5)=-4+8 = 4$. So $A'(-4,4)$.

Step3: Rotate point B

For point $B(-7,3)$ with $(h,k)=(-5,-4)$:
$x=-7,y = 3$.
$x_{new}=-5+(3 + 4)=-5+7 = 2$.
$y_{new}=-4-(-7 + 5)=-4+2=-2$. So $B'(2,-2)$.

Step4: Rotate point C

For point $C(-6,-2)$ with $(h,k)=(-5,-4)$:
$x=-6,y=-2$.
$x_{new}=-5+(-2 + 4)=-5+2=-3$.
$y_{new}=-4-(-6 + 5)=-4 + 1=-3$. So $C'(-3,-3)$.

Answer:

$A'(-4,4),B'(2,-2),C'(-3,-3)$