Question

What is the dilation (scaling) factor? Assume triangle ABC is the pre-image.

1/2
3
2
1/3

Answer 1

Scale factor is known as rate of change in shape or dimensions .

• If original dimension be d
• Scaled dimension be D

Then

Scale factor:-

• k=D/d

Now

Here

• BC=4
• EF=8

So

• k=8/4=2

Answer 2

2

Explanation:

The scale factor can either increase the size of an object or decrease the size of an object.

From inspection of the image, we can see that the object (ΔABC) has increased.

General formula to find the scale factor of a dilated figure:

`\mathsf{Scale\ factor = (Dimension\ of\ new\ shape)/(Dimension\ of\ original\ shape)}`

We can see that the corresponding angles between ΔABC and ΔDEF are the same. Therefore, we just need to choose one similar side of each triangle and input the length into the above formula to determine the scale factor.

Sides chosen:

• AB = 6
• DE = 12

`\mathsf{Scale\ factor = (DE)/(AB)=(12)/(6)=2}`

Therefore, the dilation (scale) factor is 2.