Algebraic Representations of Transformations Day 2

Warm Up

Triangle PQR has vertices P (3, 3), Q (5, -1), and R (1, -2). Find the

vertices of triangle P’Q’R’ after a translation of 3 units to the left and 1 unit up. Then graph the triangle

and its image.

Which coordinate changes and how does it change as you

translate a vertex right? Left? Up? Down?

How does the distance between vertices of the image change as

compared to the distance between vertices in the preimage?

Triangle PQR has vertices P (3, 3), Q (5, -1), and R (1, -3). Find the

vertices of triangle P’Q’R’ after a reflection across the y-axis. Then graph the triangle and its image.

Triangle PQR has vertices P (3, 3), Q (5, -1), and R (1, -3). Find the

vertices of triangle P’Q’R’ after a 90° counterclockwise rotation

about the origin. Then graph the triangle and its image.

Mitchell says the point (0, 0) does not change when reflected across the x- or y-axis or when rotated about the origin. Do you agree

with Mitchell? Explain why or why not.

Exit TicketTriangle ABC has vertices A(-4, 1), B(-2, 1), and C(-1, -2).

1. Find the coordinates of the vertices of triangle A’B’C’ after a 90° clockwise rotation about the origin.

2. Find the coordinates of the vertices of triangle A’B’C’ after triangle ABC is reflected across the y-axis.

3. Find the coordinates of the vertices of triangle A’B’C’ after triangle ABC is translated using the rule (x, y) → (x + 5, y - 3). Then, describe the translation.

4. Point M has coordinates (3, -2). The coordinates of point M’ after a single transformation are (-3, 2). Name a transformation that could have done this.