L5 Transformations: Rotations and Translations
Completion requirements
Unit A: Geometry
Chapter 2: Transformations
Two-Step Transformations Involving Rotations and Translations
Translate quadrilateral QRST horizontally 5 units to the right and vertically 4 units up and then rotate the image, Q'R'S'T', 90° counterclockwise. State the coordinates of each vertex of the transformed quadrilateral, Q"R"S"T", after the two transformations have been completed.
Step 1: Translation
Quadrilateral QRST is horizontally translated 5 units to the right and vertically 4 units up to produce quadrilateral Q'R'S'T'.
Step 2: Rotate quadrilateral Q'R'S'T' 90° counterclockwise to produce image Q"R"S"T". To find the coordinates of the image, first switch the x and y values. The image is quadrant 3 (bottom left), so the x values are negative and the y values are negative.
The coordinates of quadrilateral Q"R"S"T" are Q"(–6, –6), R"(–8, –5), S"(–9, –1), T"(–5, –4) after the translation and rotation have occurred.
Quadrilateral QRST is horizontally translated 5 units to the right and vertically 4 units up to produce quadrilateral Q'R'S'T'.
Step 2: Rotate quadrilateral Q'R'S'T' 90° counterclockwise to produce image Q"R"S"T". To find the coordinates of the image, first switch the x and y values. The image is quadrant 3 (bottom left), so the x values are negative and the y values are negative.
The coordinates of quadrilateral Q"R"S"T" are Q"(–6, –6), R"(–8, –5), S"(–9, –1), T"(–5, –4) after the translation and rotation have occurred.