To define transformation rules based on the provided pre-image and image points, we can look for patterns in the coordinates of the points. Here are two transformation rules, with one rule being incorrect:
Transformation Rule 1 (Correct)
This rule focuses on translating the \(x\) coordinate by subtracting 7 and keeping the \(y\) coordinate unchanged.
Rule:
\(A(x, y) \to A'(x - 7, y)\)
Verification:
-
For point A(3, 2):
\(A'(3-7, 2) = A'(-4, 2)\) (matches) -
For point B(6, 3):
\(B'(6-7, 3) = B'(-1, 3)\) (matches) -
For point C(7, 1):
\(C'(7-7, 1) = C'(0, 1)\) (matches)
Transformation Rule 2 (Incorrect)
This rule incorrectly suggests a transformation rule based on arbitrary changes rather than following the pattern.
Rule:
\(A(x, y) \to A'(x + 2, y + 1)\)
Verification:
-
For point A(3, 2):
\(A'(3+2, 2+1) = A'(5, 3)\) (does NOT match A'(-4, 2)) -
For point B(6, 3):
\(B'(6+2, 3+1) = B'(8, 4)\) (does NOT match B'(-1, 3)) -
For point C(7, 1):
\(C'(7+2, 1+1) = C'(9, 2)\) (does NOT match C'(0, 1))
Summary
- Transformation Rule 1 correctly describes the transformation observed in the pairs of points, while
- Transformation Rule 2 is incorrect and does not match any of the transformed coordinates.
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