When applying multiple transformations, go step-by-step in the order given.
Example Problem
Let’s say we have a triangle with points:
A = (2, -3), B = (4, -5), C = (6, -3)
And we are instructed to:
Rotate the triangle 90° counterclockwise around the origin. Translate the triangle 3 units left and 2 units up.
Step 1: Apply the 90° Counterclockwise Rotation
Using the rotation rule \( (x, y) --> (-y, x) \):
A = (2, -3) → A' = (3, 2)
B = (4, -5) → B' = (5, 4)
C = (6, -3) → C' = (3, 6)
Now, our points after the rotation are:
A' = (3, 2), B' = (5, 4), C' = (3, 6)
Step 2: Apply the Translation (3 units left and 2 units up)
Translation rule: \( (x, y) --> (x - 3, y + 2) \)
A' = (3, 2) → A'' = (0, 4)
B' = (5, 4) → B'' = (2, 6)
C' = (3, 6) → C'' = (0, 8)
After both transformations, our final coordinates are:
A'' = (0, 4), B'' = (2, 6), C'' = (0, 8)
Practice Tips
Write out each step: For each transformation, write out the transformation rule, apply it to each point, and write down the new coordinates. Graph each stage: If you’re unsure, try graphing the intermediate steps to see how each transformation affects the shape. Double-check the order: The order of transformations matters! A rotation followed by a reflection will yield a different result than a reflection followed by a rotation.