Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Please verify your account before proceeding.

In this lesson, we will learn how to identify reflection, rotation, and dilation matrices and how to use them to perform transformations of points on a plane.

Q1:

A translation of 3 units right and 2 units down can be described by the vector .

Describe the translation from point to point using a vector.

The point is translated using the vector . What are the coordinates of its image?

Q2:

Consider the given figure.

The points , , , and are corners of the unit square. This square is reflected in the line with equation to form the image .

As is the image of in the line through and , . Use this fact and the identity to find the gradient and hence equation of from the gradient of .

Using the fact that is perpendicular to , find the equation of .

Using the fact that , find the coordinates of and .

Using the fact that a reflection in a line through the origin is a linear transformation, find the matrix which represents reflection in the line .

Q3:

A linear transformation of a plane sends the vector to . If the transformation is a rotation, where does it send ?

Q4:

Let 𝑇 ∈ 𝐿 ( 𝑉 ) be a linear transformation. Suppose the matrix for 𝑇 relative to a basis 𝐵 for 𝑉 is 𝑀 . Suppose 𝑃 is the transition matrix from another basis 𝐶 to 𝐵 . Determine the matrix for 𝑇 with respect to 𝐶 .

Q5:

Shape A has been translated to Shape B and then to Shape C.

Write a vector to represent the translation from Shape A to Shape B.

Write a vector to represent the translation from Shape B to Shape C.

Write a vector to represent the translation from Shape C to Shape A.

Don’t have an account? Sign Up