Question

Triangle ABC has coordinates A (0, 4), B (1, 3), and C (-2, 4). If triangle ABC is reflected over the x axis and then translated such that (x, y) → (x+3, y-1), what is the resulting image of point C?

Answer 1

The resulting image of point C is C''(x, y) = (1, - 5).

What are the coordinates of the image of a point by using a rigid transformation?

The triangle seen on the Cartesian plane is generated by three points on that plane. The image of the triangle is the result of reflecting the three vertices over the x axis and later translating them 3 units in the +x direction and a unit in the - y direction, two kinds of rigid transformations.

Now we proceed to show the entire procedure:

Reflection over the x-axis

C'(x, y) = C(x, y) + (0, - 2 · c)

C'(x, y) = (- 2, 4) + (0, - 8)

C'(x, y) = (- 2, - 4)

Translation

C''(x, y) = (- 2, - 4) + (3, - 1)

C''(x, y) = (1, - 5)

The resulting image of point C is C''(x, y) = (1, - 5).

To learn more on rigid transformations: https://brainly.com/question/1761538

#SPJ1