Aparallelogram has coordinates a(1,1), b(5,4), c(7,1), and d(3,-2) what are the coordinates of parallelogram a’bcd after 180 degree rotation about the origin and a translation 5 units to the right and 1 unit down ?

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)

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step-by-step explanation:

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