Given rectangles ABCD and A'B'C'D, describe the transformation that takes place from ABCD to A'B'C'D'
1 answer:
Answer:
<h2>A 90° clockwise rotation about the origin and a translation of 7 units down.</h2>Step-by-step explanation:
First of all, we need to define the image and pre-image.
- The pre-image is the rectangle ABCD, before the transformation.
- The image is the rectangle A'B'C'D', after the transformation.
Second, let's write down the coordinates of each rectangle.
ABCD coordinates:
A(-6,5)
B(-1,5)
C(-1,1)
D(-6,1)
A'B'C'D' coordinates:
A'(5,-1)
B'(5,-6)
C'(1,-6)
D'(1,-1)
The first rule we need to apply is the 90° clockwise rotation which is
Which gives us (5,6), (5,1), (1,1), (1,6).
Then, we use the 7 units-down rule
Which gives us (5,-1), (5,-6), (1,-6) and (1,-1).
Therefore, the right answer is the third choice.
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We have another given root: 4.
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Now we have our second one. We can combine them:
I use elimination method which is easier here.
Multiply the top equation by -1:
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So, the answers are
and 
.
When we plug in 1, we get:
Simplify:
We got our first statement about the values of the variables. If we find one more we can find those 2 variables.
We have another given root: 4.
Plug it in:
Now we have our second one. We can combine them:
I use elimination method which is easier here.
Multiply the top equation by -1:
Add them up:
Simplify:
Now we have a, we can plug in one of those equations to find b:
So, the answers are