Dilations in the Plane

In this geometry lesson, students collect and analyze data as they investigate relationships between the pre-image and the image of a triangle. They investigate angle measures, side lengths, and the dilation factor. The dynamic nature of...

The coordinate plane is a popular place! Identify rotations, reflections, and dilations on the coordinate plane. Pupils work in small groups to match transformations of a figure with the description of the transformation. They perform...

Applying a learned technique to a new type of problem is an important skill in mathematics. The lesson asks scholars to apply their understanding to analyze dilations of different figures. They make conjectures and conclusions to...

Do you view proofs as an essential geometric skill? The resource builds on an understanding of dilations by proving the Dilation Theorem of Segments. Pupils learn to question and verify rather than make assumptions. 

The matrix — it's not just a movie. The lesson introduces the concept of 2 x 2 matrix multiplication as a way to represent linear transformations. Class members determine when a linear transformation represented as matrix multiplication...

Is that drawn to scale? Capture the artistry of geometry using the ratio method to create dilations. Mathematicians use a center and ratio to create a scaled drawing. They then use a ruler and protractor to verify measurements. 

Understanding how functions transform is a key concept in mathematics. This introductory lesson makes a strong connection between the function, table, and graph when exploring transformations. While the resource uses absolute value...

Multiplication in polar form is nice and neat—that is not the case for coordinate representation. Multiplication by a complex number results in a dilation and a rotation in the plane. The formulas to show the dilation and rotation are...

Can you follow a composition of transformations, or better yet construct them? Young mathematicians analyze the composition of dilations, examining both the scale factor and centers of dilations. They discover relationships for both and...

Class members make a real connection to matrices in the 25th part of a series of 32 by looking at the identity matrix and making the connection to the multiplicative identity in the real numbers. Pupils explore different matrices and...