Answer:
(c)
Explanation:
Given
See attachment for rectangles ABCD and A'B'C'D
Required
Determine two possible ways of transformation
From the attachment, we have:
ABCD coordinates:
[tex]A = (-6,5)[/tex]
[tex]B = (-1,5)[/tex]
[tex]C = (-1,1)[/tex]
[tex]D = (-6,1)[/tex]
A'B'C'D' coordinates:
[tex]A' = (5,-1)[/tex]
[tex]B' = (5,-6)[/tex]
[tex]C' = (1,-6)[/tex]
[tex]D' = (1,-1)[/tex]
The first transformation is a rotation of ABCD by 90 degrees using the rule:
(x,y) => (y,-x)
So, we have:
[tex]A = (-6,5)[/tex] ===> [tex](5,6)[/tex]
[tex]B = (-1,5)[/tex] ===> [tex](5,1)[/tex]
[tex]C = (-1,1)[/tex] ===> [tex](1,1)[/tex]
[tex]D = (-6,1)[/tex] ===> [tex](1,6)[/tex]
Next, is to translate 7 units down using the rule
(x,y) => (x,y-7)
So, we have:
[tex](5,6)[/tex] ==> [tex](5,6-7)[/tex]
[tex](5,1)[/tex] ==> [tex](5,1-7)[/tex]
[tex](1,1)[/tex] ==> [tex](1,1-7)[/tex]
[tex](1,6)[/tex] ==> [tex](1,6-7)[/tex]
This gives
[tex]A' = (5,-1)[/tex]
[tex]B' = (5,-6)[/tex]
[tex]C' = (1,-6)[/tex]
[tex]D' = (1,-1)[/tex]
Option (c) is correct
