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A line segment has endpoints at $(5, 8)$ $(5 , 8)$ and $(6, 1)$ $(6 , 1)$ . If the line segment is rotated about...
A line segment has endpoints at $(5, 2)$ $(5 , 2)$ and $(3, 1)$ $(3 , 1)$ . If the line segment is rotated about...
A line segment has endpoints at $(5, 2)$ $(5 , 2)$ and $(3, 1)$ $(3 , 1)$ . If the line segment is rotated about...
A line segment has endpoints at $(8, 4)$ $(8 , 4)$ and $(1, 2)$ $(1 , 2)$ . If the line segment is rotated about...
A line segment has endpoints at $(8, 4)$ $(8 , 4)$ and $(1, 2)$ $(1 , 2)$ . If the line segment is rotated about...
A line segment has endpoints at $(2, 3)$ $(2 , 3)$ and $(1, 2)$ $(1 , 2)$ . If the line segment is rotated about...
A line segment has endpoints at $(2, 3)$ $(2 , 3)$ and $(1, 2)$ $(1 , 2)$ . If the line segment is rotated about...
A line segment has endpoints at $(2, 3)$ $(2 , 3)$ and $(5, 2)$ $(5 , 2)$ . If the line segment is rotated about...
A line segment has endpoints at $(2, 2)$ $(2 , 2)$ and $(5, 4)$ $(5 , 4)$ . If the line segment is rotated about...
A line segment has endpoints at $(2, 2)$ $(2 , 2)$ and $(5, 4)$ $(5 , 4)$ . If the line segment is rotated about...

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Answer 1 · 2017-01-04T09:45:32

$(x, y) \to (x + 3, y - 4)$ $(x,y)->(x+3,y-4)$ translates
$(x, y) \to (- x, - y)$ $(x,y)->(-x,-y)$ rotates

If two figures are congruent in the plane, then they can be superposed exactly by a set of translations and rotations. The transformations

$(x, y) \to (3 x, 3 y)$ $(x,y)->(3x,3y)$ expands
$(x, y) \to (0.4 x, 0.4 y)$ $(x,y)->(0.4x,0.4y)$ shrinks

and the transformations

$(x, y) \to (x + 3, y - 4)$ $(x,y)->(x+3,y-4)$ translates
$(x, y) \to (- x, - y)$ $(x,y)->(-x,-y)$ rotates

so those two last transformations generate congruent equivalents.