A polygon has coordinates A(-7, 8), B(-4, 6), C(-4, 3), D(-8, 3), and E(-9, 6). What are the coordinates of its image, polygon A′B′C′D′E′, after a 270° counterclockwise rotation about the origin and a translation 2 units to the left and 3 units up? A′(-6, 10), B′(-4, 7), C′(-1, 7), D′(-1, 11), E′(-4, 12) A′(6, 10), B′(4, 7), C′(1, 7), D′(1, 11), E′(4, 12) A′(5, 11), B′(3, 8), C′(0, 8), D′(0, 12), E′(3, 13) A′(-5, 11), B′(-3, 8), C′(0, 8), D′(0, 12), E′(-3, 13)

Answer:A' = (6 , 10) , B' = (4 , 7) , C' = (1 , 7) , D' = (1 , 11) , E' = (2 , 12)Step-by-step explanation:* Lets revise the rotation and translation- If point (x , y) rotated about the origin by angle 90° counterclockwise  ∴ Its image is (-y , x)- If point (x , y) rotated about the origin by angle 180° counterclockwise  ∴ Its image is (-x , -y)- If point (x , y) rotated about the origin by angle 270° counterclockwise  ∴ Its image is (y , -x)- If the point (x , y) translated horizontally to the right by h units  ∴ Its image is (x + h , y)- If the point (x , y) translated horizontally to the left by h units  ∴ Its image is (x - h , y)- If the point (x , y) translated vertically up by k units  ∴ Its image is (x , y + k)- If the point (x , y) translated vertically down by k units  ∴ Its image is (x , y - k)* Now lets solve the problem- The vertices of the polygon are:   A = (-7 , 8) , (B = (-4 , 6) , C = (-4 , 3) , D = (-8 , 3) , E = (-9 , 6)- The polygon rotates 270° counterclockwise about the origin∵ Point (x , y) rotated about the origin by angle 270° counterclockwise ∴ Its image is (y , -x)∵ A = (-7 , 8) ∴ Its image = (8 , 7)∵ B = (-4 , 6) ∴ Its image = (6 , 4)∵ C = (-4 , 3) ∴ Its image = (3 , 4)∵ D = (-8 , 3) ∴ Its image = (3 , 8)∵ E = (-9 , 6) ∴ Its image = (6 , 9)- After the rotation the image will translate 2 units to the left and  3 units up∴ We will subtract 2 units from each x-coordinates of the vertices and   add 3 units to each y-coordinates of the vertices∵ Point (x , y) translated horizontally to the left by h units∴ Its image is (x - h , y)∵ Point (x , y) translated vertically up by k units∴ Its image is (x , y + k)∴ A' = (8 - 2 , 7 + 3)∴ A' = (6 , 10)∴ B' = (6 - 2 , 4 + 3)∴ B' = (4 , 7)∴ C' = (3 - 2 , 4 + 3)∴ C' = (1 , 7)∴ D' = (3 - 2 , 8 + 3)∴ D' = (1 , 11)∴ E' = (6 - 2 , 9 + 3)∴ E' = (4 , 12)* The coordinates of its image are:   A' = (6 , 10) , B' = (4 , 7) , C' = (1 , 7) , D' = (1 , 11) , E' = (2 , 12)