The images of the points R(x, y) = (2, - 1) and S(x, y) = (6, - 5) are R''(x, y) = (0, - 3) and S''(x, y) = (- 4, - 7), respectively.
How to find the image of a given set of points
In this problem we must determine the image of two points by a sequence of rigid transformations, which are now defined:
Translation: P'(x, y) = P(x, y) + T(x, y)
Reflection about y-axis: P'(x, y) = (x, y) → P''(x, y) = (- x, y)
Now we proceed to determine the images of the two points set on Cartesian plane: R(x, y) = (2, - 1), S(x, y) = (6, - 5)
Translation:
R'(x, y) = (2, - 1) + (- 2, - 2)
R'(x, y) = (0, - 3)
S'(x, y) = (6, - 5) + (- 2, - 2)
S'(x, y) = (4, - 7)
Reflection about y-axis:
R''(x, y) = (0, - 3)
S''(x, y) = (- 4, - 7)
Finally we present the points on Cartesian plane.