Question

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

Explanation:

Step1: Translate points relative to pivot

First, translate points A, B, C so that the pivot point (-5, -4) is at the origin. For a point (x, y) and pivot (p_x, p_y), the translated point (x', y') is given by x'=x - p_x and y'=y - p_y.
For A(-13, -3): x_A'=-13-(-5)=-8, y_A'=-3 - (-4)=1
For B(-7, 3): x_B'=-7-(-5)=-2, y_B'=3 - (-4)=7
For C(-6, -2): x_C'=-6-(-5)=-1, y_C'=-2 - (-4)=2

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 the translated point of A (-8, 1): After rotation, x_A'' = 1, y_A''=8
For the translated point of B (-2, 7): After rotation, x_B'' = 7, y_B''=2
For the translated point of C (-1, 2): After rotation, x_C'' = 2, y_C''=1

Step3: Translate points back

Now, translate the rotated points back to the original coordinate system. The formula is x = x''+p_x and y = y''+p_y.
For the rotated point of A: x_A'=1+(-5)=-4, y_A'=8+(-4)=4
For the rotated point of B: x_B'=7+(-5)=2, y_B'=2+(-4)=-2
For the rotated point of C: x_C'=2+(-5)=-3, y_C'=1+(-4)=-3

Answer:

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