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Triangle Coordinates After Reflection and Mapping

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Triangle abc has coordinates a(-1,3), b(-6,5), and c(-4,7):
1- The coordinates of triangle a'b'c', the image of triangle abc after a reflection in the x-axis are a'------, ----- b'-----, ----- c'-----, -----?
2- The coordinates of triangle a''b''c'', the image of triangle abc after a reflection in the line y=x, are a''-----, ----- b''-----, ----- c''----, -----?
3- The coordinates of triangle a'''b'''c''', the image of triangle abc under the translation which maps (x,y) to (x+8,y+3) are, a'''----, ---- b'''----,---- c'''-----,-----?

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The solution gives detailed steps on finding the coordinates of triangle after different reflections and mapping. All formula and calculations are shown and explained.

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1- The coordinates of triangle a'b'c', the image of triangle abc after a reflection in the x-axis are a'------, ----- b'-----, ----- c'-----, -----?
Ans: for reflection in the x-axis, we only change ...

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