Question

Write a sequence of transformation that maps quadrilateral ABCD onto quadrilateral A. B. C. D IN THE PICTURE

Answer 1

Answer:

The sequence of transformation is reflected across the y-axis and translated 2 units down

Step-by-step explanation:

Lets revise some transformation

- If point (x , y) reflected across the x-axis

∴ Its image is (x , -y)

- If point (x , y) reflected across the y-axis

∴ Its image is (-x , y)

- If point (x , y) translate h units to the right

∴ Its image is (x + h , y)

- If point (x , y) translate h units to the left

∴ Its image is (x - h , y)

- If point (x , y) translate k units up

∴ Its image is (x , y + k)

- If point (x , y) translate k units down

∴ Its image is (x , y - k)

* Now lets solve the problem

∵ The vertices of figure ABCD are:

  A (-1 , 3) , B (1 , 0) , C (2 , 3) , D (1 , 4)

∵ The vertices of figure A"B"C"D" are:

  A" (1 , 1) , B" (-1 , -2) , C" (-2 , 1) , D" (-1 , 2)

* Lets compare between ABCD and A"B"C"D"

∵ All x-coordinates has opposite signs

  -1 ⇒ 1 , 1 ⇒ -1 , 2 ⇒ -2 , 1 ⇒ -1

∴ The ABCD is reflected across the y-axis

∵ All y-coordinates subtracted by 2

 3 ⇒ 1 , 0 ⇒ -2 , 3 ⇒ 1 , 4 ⇒ 2

∴ The ABCD is translated 2 units down

* The sequence of transformation is reflected across the y-axis

  and translated 2 units down