Question

Triangle ABC goes through a sequence of transformations to form Triangle DEF. It is first reflected over the x-axis. Then, rotated 90° counterclockwise. Finally, it is translated up 4 units. What are the coordinates of triangle DEF?

A. (x, y)
B. (x - 4, y)
C. (-x, -y)
D. (-x + 4, -y)

Answer 1

To find the coordinates of triangle DEF after the given sequence of transformations, reflect over the x-axis, then rotate 90° counterclockwise, and finally translate up 4 units.

Step-by-step explanation:

To find the coordinates of triangle DEF after the given sequence of transformations, we need to start with the coordinates of triangle ABC and apply each transformation step by step.

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

First, reflect over the x-axis: The new coordinates will be A(x1, -y1), B(x2, -y2), C(x3, -y3).

Next, rotate 90° counterclockwise: The new coordinates will be A(-y1, x1), B(-y2, x2), C(-y3, x3).

Finally, translate up 4 units: The new coordinates will be A(-y1, x1 + 4), B(-y2, x2 + 4), C(-y3, x3 + 4).

So, the coordinates of triangle DEF are (-y1, x1 + 4), (-y2, x2 + 4), (-y3, x3 + 4).