Question

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

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 A(-13,-3) relative to (-5,-4): $x_1=-13-(-5)=-8$, $y_1=-3 - (-4)=1$.
For point B(-7,3) relative to (-5,-4): $x_2=-7-(-5)=-2$, $y_2=3 - (-4)=7$.
For point C(-6,-2) relative to (-5,-4): $x_3=-6-(-5)=-1$, $y_3=-2 - (-4)=2$.

Step2: Apply 90 - degree clockwise rotation formula

The formula for a 90 - degree clockwise rotation of a point $(x,y)$ is $(y,-x)$.
For the relative - coordinates of A: The new relative - coordinates are $(1,8)$.
For the relative - coordinates of B: The new relative - coordinates are $(7,2)$.
For the relative - coordinates of C: The new relative - coordinates are $(2,1)$.

Step3: Translate back to original coordinate system

To get the final coordinates $(X,Y)$ after rotation, use the formula $X=a + x_{new}$ and $Y=b + y_{new}$, where $(a,b)=(-5,-4)$.
For point A: $X=-5 + 1=-4$, $Y=-4+8 = 4$.
For point B: $X=-5 + 7=2$, $Y=-4 + 2=-2$.
For point C: $X=-5+2=-3$, $Y=-4 + 1=-3$.

Answer:

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