Answer:
The coordinates are (4 , -2) , (0 , -5) , (-2 , -2) , (2 , 1)
Step-by-step explanation:
* Lets revise some transformation
- If point (x , y) rotated about the origin by angle 180°
∴ Its image is (-x , -y)
- 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
∵ ABCD is a parallelogram
∵ Its vertices are A (1 , 1) , B (5 , 4) , C (7 , 1) , D (3 , -2)
∵ The parallelogram rotates about the origin by 180°
∵ The image of the point (x , y) after rotation 180° about the origin
is (-x , -y)
∴ The images of the vertices of the parallelograms are
(-1 , -1) , (-5 , -4) , (-7 , -1) , (-3 , 2)
∵ The parallelogram translate after the rotation 5 units to the right
and 1 unit down
∴ We will add each x-coordinates by 5 and subtract each
y-coordinates by 1
∴ A' = (-1 + 5 , -1 - 1) = (4 , -2)
∴ B' = (-5 + 5 , -4 - 1) = (0 , -5)
∴ C' = (-7 + 5 , -1 - 1) = (-2 , -2)
∴ D' = (-3 + 5 , 2 - 1) = (2 , 1)
* The coordinates of the parallelograms A'B'C'D' are:
(4 , -2) , (0 , -5) , (-2 , -2) , (2 , 1)
