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
and 
:
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and mnp=24.