Grade 8

3.04 Translations on the coordinate plane

Lesson

Translations

A translation is what occurs when we move an object or shape from one place to another without changing its size, shape or orientation. Sometimes called a slide, a translation moves every point on an object or shape the same distance in the same direction.

To identify and describe a translation

Look for corresponding points on the object
Identify if the object has moved horizontally or vertically, and then describe that movement as left/right or up/down
Count the number of places (or units) that the object has moved

Worked example

Question 1

Describe the translation from the preimage A to the image B.

Think: First, we need to look for corresponding points on the preimage and image. Next we need to identify the direction the preimage was moved. Finally, we need to state how far it moved in each direction.

Do:

Notice the highlighted pair of corresponding points in yellow
We can see that the shape has a horizontal translation and that the preimage A has to move left to become image B.
Counting the units using the corresponding points we can see that object A has moved 3 units.

So the translation from A to B is 3 units left.

Reflect: If we know how we got from A to B, can we quickly determine how to go from B back to A?

Exploration

This applet shows the translation of an object to its image. You can use the sliders to change the horizontal and vertical amounts.

Created with Geogebra

Practice questions

Question 2

What is the translation from triangle $B$B to triangle $A$A?

Two shaded triangles positioned on a grid. The triangle on the left is shaded green and labeled B, while the triangle on the right is shaded purple and labeled A. Both triangles are identical in shape and size; their only difference is their position on the grid.

$2$2 units $left$
A
$2$2 units $right$
B
$3$3 units $left$
C
$3$3 units $right$
D

Question 3

What is the translation from square $B$B to square $A$A?

Two identically shaped square, labeled A and B are placed on a grid. Square $A$`A` is shaded in purple and square $B$`B` which shaded in green. Square $A$`A` is on the bottom and square $B$`B` is on the top.

$3$3 units $up$
A
$3$3 units $down$
B
$4$4 units $up$
C
$4$4 units $down$
D

Question 4

What is the translation from quadrilateral $A$ to quadrilateral $B$ ?

In the Cartesian coordinate place, two quadrilaterals are graphed side by side labeled as $A$`A` and $B$`B`. Quadrilateral $A$`A` is shaded green. Quadrilateral $B$`B` of the same shape is shaded blue. Quadrilateral $A$`A` is on the bottom-right side of quadrilateral $B$`B`.

$2$2 units $left$ and $4$4 units $down$
A
$4$4 units $left$ and $2$2 units $down$
B
$2$2 units $right$ and $4$4 units $up$
C
$4$4 units $right$ and $2$2 units $up$
D

Outcomes

8.G.A.3

Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.