Answer:
(1, - 1 )
Step-by-step explanation:
A translation of 2 down means subtract 2 from the y- coordinate
(- 1, 3 ) → (- 1, 3 - 2 ) → (- 1, 1 )
Under a counterclockwise rotation about the origin of 180°
a point (x, y ) → (- x, - y ) , then
(- 1, 1 ) → (1, - 1 )
Overall
(- 1, 3 ) → (- 1, 1 ) → (1, - 1 )
The image of (-1, 3) was obtained by translating 2 units down, followed by a rotation of 180° counterclockwise about the origin is (1,-1).
A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.
The given point with coordinates of (-1,3), when translated downwards will have the coordinated equal,
(-1,3) ⇒ (-1, 3-2) ⇒ (-1, 1)
Now, since the translation is about 180° in the counter-clockwise direction, the coordinates of the new point will be equal to,
(-1,1) ⇒ (1, -1)
Hence, the image of (-1, 3) obtained by translating 2 units down, followed by a rotation of 180° counterclockwise about the origin is (1,-1).
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