To find the coordinates of point C after the given transformations, we start with the original coordinates of point C, which are (3, -5).
Step 1: Translation
The translation involves moving the point 4 units left and 1 unit down.
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Moving 4 units left:
- The x-coordinate decreases by 4: \( x = 3 - 4 = -1 \)
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Moving 1 unit down:
- The y-coordinate decreases by 1: \( y = -5 - 1 = -6 \)
After the translation, the new coordinates of point C are: \[ (-1, -6) \]
Step 2: Reflection over the y-axis
When reflecting a point over the y-axis, the x-coordinate changes sign while the y-coordinate remains the same.
For the point \((-1, -6)\):
- The x-coordinate becomes: \( x = -(-1) = 1 \)
The y-coordinate remains: \( y = -6 \)
Thus, after the reflection, the coordinates of point C are: \[ (1, -6) \]
Given the answer choices:
a) (-3, 2)
b) (2, 1)
c) (3, -5)
d) (-6, -2)
None of the answer choices match (1, -6). If you have additional context or constraints regarding the original point C or the transformation process, please share them!