reflection matrix


Definition of Reflection Matrix

  • A matrix that is used to reflect an object over a line or plane is called a reflection matrix.

Examples of Reflection Matrix

  • The figure below shows the reflection of triangle ABC about the y-axis.
     is the reflection matrix for the y-axis.

Solved Example on Reflection Matrix

Find the coordinates of the vertices of the image of triangle ABC with A(1, 3), B(-1, 1), C(3, 1) after a reflection across the y-axis.
Choices:
A. A′(- 1, 3), B′(1, 1), C′(- 3, 1)
B. A′(- 1, - 3), B′(1, 1), C′(- 3, 1)
C. A′(- 1, 3), B′(1, - 1), C′(- 3, 1)
D.A′(- 1, 3), B′(1, 1), C′(3, 1)
Correct Answer: A
Solution:
Step 1: The coordinates of the vertices of triangle ABC are given by A(1, 3), B(-1, 1), C(3, 1).
Step 2: Then multiply the vertex matrix by reflection matrix for the y-axis
  =

Step 3: Therefore, the coordinates of the vertices of ABC′ are A′(- 1, 3), B′(1, 1), C′(- 3, 1).     

Related Terms for Reflection Matrix

  • Plane
  • Line
  • Matrix
  • Reflection