What translation rule can be used to describe the result of the composition of (x, y) --> (x – 9, y – 2) and (x, y) --> (x + 1, y – 2)?
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1 point
(x, y) --> (x + 8, y – 4)
(x, y) --> (x – 10, y + 0)
(x, y) --> (x – 8, y – 4)
(x, y) --> (x – 4, y – 8)
The translation rule that can be used to describe the result of the composition of (x, y) --> (x – 9, y – 2) and (x, y) --> (x + 1, y – 2) is:
(x, y) --> (x – 8, y – 4)
Which type of symmetry is shown by the lowercase letter w?
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1 point
reflectional symmetry
point symmetry
no symmetry
rotational symmetry
The lowercase letter "w" exhibits reflectional symmetry.
To find the result of the composition of two translation rules, we need to apply the second translation rule first, and then apply the first translation rule to the result.
Let's start with the second translation rule: (x, y) --> (x + 1, y – 2)
This rule translates a point (x, y) by adding 1 to the x-coordinate and subtracting 2 from the y-coordinate.
Now, let's apply the first translation rule to the result of the second rule: (x – 9, y – 2)
This rule translates a point (x, y) by subtracting 9 from the x-coordinate and subtracting 2 from the y-coordinate.
So, the composition of the two translation rules is:
(x, y) --> (x – 9, y – 2) after (x, y) --> (x + 1, y – 2)
By substituting the values from the second rule into the first rule, we get:
(x – 9, y – 2) --> ((x – 9) + 1, (y – 2) – 2)
Simplifying this expression:
(x – 9, y – 2) --> (x – 8, y – 4)
Therefore, the translation rule that describes the result of the composition is:
(x, y) --> (x – 8, y – 4)
So, the correct answer is (x, y) --> (x – 8, y – 4).