Question

Explain in detail the procedure to translate triangle ABC in the direction and distance of CC’ and then reflect it across the y-axis. Be specific and use mathematical language. What are the coordinates for the image of triangle ABC after both transformations?

a) Translate: (x, y) -> (x+CC', y); Reflect: (x, y) -> (-x, y); Image coordinates: ...
b) Translate: (x, y) -> (x+CC', y); Reflect: (x, y) -> (x, -y); Image coordinates: ...
c) Translate: (x, y) -> (x, y+CC'); Reflect: (x, y) -> (-x, y); Image coordinates: ...
d) Translate: (x, y) -> (x, y+CC'); Reflect: (x, y) -> (x, -y); Image coordinates: ...

Answer 1

To translate triangle ABC in the direction and distance of CC', we will add the vector CC' to each vertex of triangle ABC. To reflect the translated triangle across the y-axis, we need to change the sign of the x-coordinate for each vertex.

Step-by-step explanation:

To translate triangle ABC in the direction and distance of CC', we will add the vector CC' to each vertex of triangle ABC.

Let's assume the coordinates of the vertices of triangle ABC are A(x1, y1), B(x2, y2), and C(x3, y3), and the coordinates of point C' are (a, b).

To translate triangle ABC to its new position, the coordinates of the new vertices are: A'(x1+a, y1+b), B'(x2+a, y2+b), and C'(x3+a, y3+b).

To reflect the translated triangle across the y-axis, we need to change the sign of the x-coordinate for each vertex.

The coordinates of the image of triangle ABC after both transformations are: A''(-x1-a, y1+b), B''(-x2-a, y2+b), and C''(-x3-a, y3+b).