To determine how the line segment LM with vertices \(L(-7, -2)\) and \(M(0, 5)\) is transformed to line segment \(L'M'\) with vertices \(L'(-2, 0)\) and \(M'(5, 7)\), we can calculate the transformation needed to map the coordinates of \(L\) and \(M\) to \(L'\) and \(M'\).
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Finding the transformation for point \(L\):
- Original point \(L(-7, -2)\)
- After transformation \(L'(-2, 0)\)
Let's find the change in each coordinate:
- For \(x\): \(-7\) is transformed to \(-2\). The change is: \[ -2 - (-7) = -2 + 7 = 5 \]
- For \(y\): \(-2\) is transformed to \(0\). The change is: \[ 0 - (-2) = 0 + 2 = 2 \]
Therefore, the transformation for point \(L\) can be described by the function: \[ (x, y) \rightarrow (x + 5, y + 2) \]
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Finding the transformation for point \(M\):
- Original point \(M(0, 5)\)
- After transformation \(M'(5, 7)\)
Let's find the change in each coordinate:
- For \(x\): \(0\) is transformed to \(5\). The change is: \[ 5 - 0 = 5 \]
- For \(y\): \(5\) is transformed to \(7\). The change is: \[ 7 - 5 = 2 \]
This confirms that the transformation for point \(M\) agrees with the transformation found for point \(L\).
Conclusion
The transformation that maps line segment LM to L'M' is represented by: \[ \text{(x, y) } \rightarrow \text{ (x + 5, y + 2)} \] Thus, the correct answer is Option A.