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)
