Rotations and Dilations
Grade 8 · Math · Geometry and the Pythagorean Theorem · Oklahoma, USA
Lesson Summary
Rotate shapes around a point and resize them using scale factors.
Explanation
A rotation turns a shape around a fixed point by a certain angle. Common rotations are 90°, 180°, and 270° around the origin. A dilation resizes a shape by multiplying every distance from the center by a scale factor. A scale factor greater than 1 makes the shape bigger, and a scale factor between 0 and 1 makes it smaller. Rotations preserve size and shape, while dilations change size but keep the same proportions.
Practice Questions
Q1: Rotate the point (3, 0) by 90° counterclockwise around the origin. Where does it go?
Answer: It moves to (0, 3). A 90° counterclockwise rotation sends (x, y) to (−y, x).
Q2: A triangle has a vertex at (2, 4). After a dilation with scale factor 3 centered at the origin, where is that vertex?
Answer: (6, 12). Multiply each coordinate by the scale factor: 2 × 3 = 6, 4 × 3 = 12.
Q3: After a dilation with scale factor 0.5, is the new shape larger or smaller?
Answer: Smaller. A scale factor less than 1 shrinks the shape to half its original size.
People Also Ask
What is Rotations and Dilations in Grade 8 Math?+
Rotations and Dilations is a lesson in the Geometry and the Pythagorean Theorem chapter of Grade 8 Math. It is part of the Oklahoma, USA school curriculum and covers key concepts that students need to understand at this level.
What grade level covers Rotations and Dilations?+
Rotations and Dilations is taught in Grade 8 as part of the Math curriculum in Oklahoma, USA.
How can I help my child with Geometry and the Pythagorean Theorem in Math?+
Start with the lesson summary and explanation on this page. Practice the questions provided, then use TutorTom for personalized, step-by-step help with Geometry and the Pythagorean Theorem topics.