Lesson: Linear Transformations in Planes: Reflection Mathematics • 10th Grade

In this lesson, we will learn how to find the matrix of linear transformation of reflection along the x- or y-axis or the line of a given equation and the image of a vector under the reflection.

Lesson Plan

Students will be able to

calculate the image of a single vector under a linear transformation that reflects in a line or axis,
calculate the image of a shape in the 2D plane under a linear transformation that reflects in a line or axis,
interpret the geometric effect of applying a given reflection matrix,
find the matrix that represents a reflection of a vector or shape
- in the - or ,
- in a line of a given equation.

Lesson Worksheet

Q1:

Which of the following are necessary and sufficient conditions on , , , and for the matrix to represent a reflection?

Q2:

A reflection in a line through the origin sends the vector to . Find the matrix representation of this reflection.

Q3:

A reflection in a line through the origin sends the vector to . Find the matrix representation of this reflection.