About the topic "Reflection transformation matrix"

"Reflection transformation matrix" is the matrix which can be used to make reflection transformation of a figure.

Even though students can get this stuff on internet, they do not understand exactly what has been explained.

To make the students to understand the stuff "Reflection transformation using matrix", we have explained the different rules which we apply to make reflection-transformation.

Rules on finding reflected image

Reflection about the x-axis

Reflection about the y-axis

Reflection about the line y=x

Once students understand the rules which they have to apply for reflection transformation, they can easily make reflection transformation of a figure.

Let us consider the following example to have better understanding of reflection.

Question :

Let A ( -2, 1), B (2, 4) and (4, 2) be the three vertices of a triangle. If this triangle is reflected about x-axis, find the vertices of the reflected image A'B'C' using matrices.

Solution:

Step 1 :

First we have to write the vertices of the given triangle ABC in matrix form as given below.

Step 2 :

Since the triangle ABC is reflected about x-axis, to get the reflected image, we have to multiply the above matrix by the matrix given below.

Step 3 :

Now, let us multiply the two matrices.

Step 4 :

Now we can get vertices of the reflected image A'B'C' from the resultant matrix.

Vertices of the reflected image are

A' (-2 , -1) , B' (2 , -4) and C' (4 , -2)

After having gone through the example given above, we hope that the students would have understood the way in which they have to find the vertices of the reflected image using matrices.

Reflecting over any line

When we look at the above figure, it is very clear that each point of a
reflected image A'B'C' is at the same distance from the line of reflection as the
corresponding point of the original figure.

In other words, the
line x = -2 (line of reflection) lies directly in the middle between the original figure and
its image.

And also, the line x = -2 (line of reflection) is the perpendicular bisector of the segment joining any
point to its image.

Students can keep this idea in mind when they are working with lines of
reflections which are neither the x-axis nor the y-axis.

After having gone through the stuff given above, we hope that the students would have understood "Reflection transformation matrix".

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