The document provides examples of performing rigid transformations on geometric shapes, including translations and reflections. Example 1 demonstrates translating a letter A by subtracting a translation vector from each point's coordinates. Example 2 shows reflecting a triangle across the x-axis by counting blocks from each vertex to the axis and plotting the image vertices on the opposite side. Example 3 reflects a triangle PQR across the lines y=1 and x=0 to obtain the images P'Q'R' and P"Q"R", using the same block counting method.

1. Finding the image after a
Rigid Transformation.
Translation, Reflection, Rotation

2. EXAMPLES

3. EXAMPLE 1 Perform a translation on the letter A using 𝑇 =
−3
2
.
Coordinates of letter A.
3, 2
4, 4
(5, 2)
To find the coordinates of the image of A:
Write the coordinates in column form then add the translation
to each one.
•
3
2
+
−3
2
=
𝟎
𝟒
•
4
4
+
−3
2
=
𝟏
𝟔
•
5
2
+
−3
2
=
𝟐
𝟒
Plot these points and join them to form the image.

4. EXAMPLE 1 cont’d.
Write the coordinates in column form then add
the translation to each one.
•
3
2
+
−3
2
=
𝟎
𝟒
•
4
4
+
−3
2
=
𝟏
𝟔
•
5
2
+
−3
2
=
𝟐
𝟒
Plot these points and join them to form the
image.

5. EXAMPLE 2
Triangle ABC is shown with vertices 𝐴 1,1 , B 1,4 , C (3, 1).
It is mapped onto triangle LMN by a reflection in the x-axis.
Draw the reflected triangle LMN.
Count the number of blocks from each vertex to the axis of
reflection.
On the other side of the axis, count the same number of
blocks and plot the corresponding image vertices.
Join them to form triangle LMN.

6. EXAMPLE 2 cont’d.

7. EXAMPLE 3
Triangle PQR is shown.
 State the coordinates of R.
 On the diagram, draw triangle 𝑃’𝑄’𝑅’, a reflection of PQR
in the line 𝑦 = 1.
 On the diagram, draw triangle 𝑃′′𝑄′′𝑅′′, a reflection of
𝑃′𝑄′𝑅′ in the line 𝑥 = 0.
 The coordinates of R (0, 3).

8. EXAMPLE 3 cont’d.
 Reflection of 𝑃′
𝑄′
𝑅′ in the line 𝑦 = 1.
Count the number of blocks from each vertex to the axis of
reflection.
On the other side of the axis, count the same number of
blocks and plot the corresponding image vertices.
Join them to form triangle 𝑃′
𝑄′
𝑅′.

9. EXAMPLE 3 cont’d.
 On the diagram, draw triangle 𝑃′′
𝑄′′
𝑅′′, a reflection of
𝑃′𝑄′𝑅′ in the line 𝑥 = 0.
Count the number of blocks from each vertex to the axis of
reflection.
On the other side of the axis, count the same number of
blocks and plot the corresponding image vertices.
Join them to form triangle 𝑃′′𝑄′′𝑅′′.

10. The End.