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More Geometry Lessons

Transformation Games

In these lessons, we will learn

### What is Dilation or Enlargement?

### Dilation with scale factor > 1

**Step 1: **Measure
OP.

**Step 2:**
Extend the line OP to the point P’ such that OP’ = 2OP.

**Step 3: **Repeat
the steps for all the vertices: point Q to get Q' and point R to
get R'.

**Step 4:**
Join the points P’Q’R’ to form the image.

**Step 1: **Measure
CA.

**Step 2: **Extend
the line CA to the point A’ such that CA’ = 3CA.

**Step 3: **Repeat
the steps for point B to get B'.

**Step 1:**
Join OP.

**Step 2: **Extend
the line OP to OP’, such that OP’ = 1.5 × OP

**Step 3:**
Repeat for all the other vertices Q, R and S.

**Step 4: **Join
P’, Q’, R’ and S’ to form the image.

**An introduction to the concepts of dilation transformations**

What happens when the scale factor or the center of the dilation is changed?

### Dilation with scale factor between 0 and 1

**Step 1 : **Join
*O* to *P*.

**Step 2 : **Mark
off the point *P* ’ on *OP* such that *OP'*
= *OP*.

**Step 3 :**
Repeat the steps for all the vertices: point *Q* to get *Q'*
and point *R* to get *R'*

**Step 4 :**
Join the points *P'**Q'**R'* to form the
image.

**Dilation of a Geometric Figure**

How to create a dilation of a geometric figure using a center of dilation and a scale factor of half?

### Dilation with a Negative Scale Factor

If the scale factor of a dilation is negative then the image will
be on the opposite side of the center of dilation compared with
the object.

**How to create a dilation of a geometric figure using a center of dilation and a negative scale factor?**

### Dilation on the Coordinate Plane

A dilation is a non-rigid transformation, which means that the original and the image are not congruent. They are, however, similar figures.

To perform dilations, a scale factor and a center of dilation are needed. If the scale factor is larger than 1, the image is larger than the original; if the scale factor is less than 1, the image is smaller than the original.**How to get the scale factor given the points of the shape and its image?**

More Geometry Lessons

Transformation Games

In these lessons, we will learn

- what is dilation or enlargement and reduction?
- dilation with scale factor greater than 1.
- dilation with scale factor between 0 and 1.
- dilation with a negative scale factor.
- dilation on the coordinate plane.

A** dilation** is a
transformation that produces an image that is the same shape as
the original, but is a different size. (The image is similar to
the original object). Dilation is a transformation in which each
point of an object is moved along a straight line. The straight
line is drawn from a fixed point called the center
of dilation. The distance the points move depends on the scale factor.
The center of dilation is the only invariant point.

Scale factor =

If the scale factor is greater than 1, the image is an **enlargement**.

If the scale factor is between 0 and 1, the image is a**
reduction**.

* Example: *

The figure shows two similar triangles PQR and P’Q’R’. Triangle P’Q’R’ is a dilation of triangle PQR. We say that
triangle PQR is transformed onto triangle P’Q’R’ by a dilation
with center at O and scale factor

We will first look at enlargements which are dilations with scale factors greater than 1

* Example: *

Enlarge triangle PQR with O as the center of dilation and a scale factor of 2.

* Solution: *

* Example: *

Enlarge triangle ABC with C as the center of dilation and a scale factor of 3.

* Solution: *

Note that in this example, all the points in the triangle have been transformed except point C, which is the only invariant point.

* Example: *

Draw an image of the figure PQRS. O is the center of dilation and the scale factor is 1.5.

* Solution: *

What happens when the scale factor or the center of the dilation is changed?

If the scale factor of a dilation is between 0 and 1, the image will be smaller than the object. It is then called a reduction.

* Example*

Enlarge triangle PQR with O as the center of enlargement and scale factor .

* Solution: *

How to create a dilation of a geometric figure using a center of dilation and a scale factor of half?

We will now look at how to create a dilation on a coordinate plane.

DilationsA dilation is a non-rigid transformation, which means that the original and the image are not congruent. They are, however, similar figures.

To perform dilations, a scale factor and a center of dilation are needed. If the scale factor is larger than 1, the image is larger than the original; if the scale factor is less than 1, the image is smaller than the original.

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