Question

Point Q is the center of dilation. Line segment L M is dilated to created line segment L prime M prime. The length of L Q is 4 and the length of Q M is 3. The length of L L prime is 4. Line segment LM is dilated to create L'M' using point Q as the center of dilation and a scale factor of 2. What is the length of segment QM'?

Answer 1

6

Explanation:

Answer 2

The length of segment QM' = 6

Explanation:

Given:

Q is the center of dilation

Pre-image (original image) = segment LM

New image = segment L'M'

The length of LQ = 4

The length of QM = 3

The length of LL' = 4

The original image was dilated with scale factor = 2

QM' = ?

To determine segment QM', first we would draw the diagram obtained from the given information.

Find attached the diagram

When a figure is dilated, we would have similar shape in thus cars similar triangles.

Segment L'M' = scale factor × length of LM

Let LM = x

L'M' = 2x

Using similar triangles theorem, ratio of their corresponding sides are equal.

QM/LM = QM'/L'M'

3/x = QM'/2x

6x = QM' × x

Q'M' = 6

The length of segment QM' = 6