The final coordinates of the triangle are A''(x, y) = (3, 2), B''(x, y) = (- 1, 4) and C''(x, y) = (2, 0), respectively.
What are the coordinates of the vertices of the image derived from transformation rules?
In this question we know the coordinates of the three vertices of the triangle, whose image must be generated by combining reflection across y-axis and translation, two kinds of rigid transformations, whose formulas are summarized below:
Reflection across y-axis
P'(x, y) = P(x, y) + (- 2 · p, 0) (1)
Translation
P'(x, y) = P(x, y) + T(x, y) (2)
Where:
- P(x, y) - Original point
- P'(x, y) - Resulting point
- T(x, y) - Translation vector
- p - x-Coordinate of the original point.
If we know that A(x, y) = (1, - 3), B(x, y) = (5, - 1) and C(x, y) = (2, - 5), then the final coordinates are:
Reflection across y-axis
A'(x, y) = (1, - 3) + (- 2, 0)
A'(x, y) = (- 1, - 3)
B'(x, y) = (5, - 1) + (- 10, 0)
B'(x, y) = (- 5, - 1)
C'(x, y) = (2, - 5) + (- 4, 0)
C'(x, y) = (- 2, - 5)
Translation
A''(x, y) = (- 1, - 3) + (4, 5)
A''(x, y) = (3, 2)
B''(x, y) = (- 5, - 1) + (4, 5)
B''(x, y) = (- 1, 4)
C''(x, y) = (- 2, - 5) + (4, 5)
C''(x, y) = (2, 0)
The final coordinates of the triangle are A''(x, y) = (3, 2), B''(x, y) = (- 1, 4) and C''(x, y) = (2, 0), respectively.
To learn more on rigid transformations: https://brainly.com/question/1761538
#SPJ1
