The double reflection generates the following three points: A''(x, y) = (1, - 1), B''(x, y) = (2, 2) and C''(x, y) = (5, 2).
How to generate a set of point by rigid transformations
In this problem we must apply two rigid transformations to find three points. The formula for reflection over an axis parallel to the y-axis is defined below:
P'(x, y) = (x', k) - [P(x, y) - (x', k)] (1)
Where:
- x' - x-coordinate of the point P(x, y).
- P(x, y) - Original point
- P'(x, y) - Resulting point
If we know that A(x, y) = (1, - 5), k = - 1 and k' = 1, then the resulting points are:
Point A
A'(x, y) = (1, - 1) - [(1, - 5) - (1, - 1)]
A'(x, y) = (1, - 1) - (0, - 4)
A'(x, y) = (1, 3)
A''(x, y) = (1, 1) - [(1, 3) - (1, 1)]
A''(x, y) = (1, 1) - (0, 2)
A''(x, y) = (1, - 1)
Point B
B'(x, y) = (2, - 1) - [(2, - 2) - (2, - 1)]
B'(x, y) = (2, - 1) - (0, - 1)
B'(x, y) = (2, 0)
B''(x, y) = (2, 1) - [(2, 0) - (2, 1)]
B''(x, y) = (2, 1) - (0, - 1)
B''(x, y) = (2, 2)
Point C
C'(x, y) = (5, - 1) - [(5, - 2) - (5, - 1)]
C'(x, y) = (5, - 1) - (0, - 1)
C'(x, y) = (5, 0)
C''(x, y) = (5, 1) - [(5, 0) - (5, 1)]
C''(x, y) = (5, 1) - (0, - 1)
C''(x, y) = (5, 2)
The double reflection generates the following three points: A''(x, y) = (1, - 1), B''(x, y) = (2, 2) and C''(x, y) = (5, 2).
To learn more on rigid transformations: https://brainly.com/question/1761538
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