Question

Line AB has a length of 5 cm. The line segment is dilated to produce line A'B', which has a length of 2 cm. Find the scale factor of the dilation.

A. k = 2/5
B. k = 1/2
C. k = 5/2
D. k = 2

Thank you in advance for your help!

Answer 1

The correct answer is A. k = 2/5

Answer 2

Option A is correct

k = 2/5

Explanation:

The rule of dilation with scale factor k is given by:

`k = \frac{\text{Image length}}{\text{original length}}`

As per the statement:

Line AB has a length of 5 cm. The line segment is dilated to produce line A'B', which has a length of 2 cm.

⇒original Length (AB)= 5 cm

and

Image length (A'B') = 2 cm

Apply the rule of dilation we have;

`k = \frac{\text{A'B'}}{\text{AB}}`

Substitute the given values;

`k = (2)/(5)`

Therefore, the scale factor of the dilation is, 2/5