Question

Given the following coordinates complete the reflection transformation.

Answer 1

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: brainly.com/question/1761538

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