# A line segment has endpoints at #(2 ,7 )# and #(5 ,4 )#. The line segment is dilated by a factor of #3 # around #(4 ,3 )#. What are the new endpoints and length of the line segment?

##### 1 Answer

Please read the explanation.

#### Explanation:

**Given:**

**Scale Factor for dilation is #3#**.

**Useful observations involving Dilation:**

**Isometry** refers to a linear transformation which preserves the length.

Dilation is **NOT an isometry**. It creates **similar figures** only.

Here **pre-image** and **after dilation**, **image**.

The **absolute value of the scale factor (k),**

with the constraint

**reduces** the line segment

**enlarges** if otherwise.

Each point on the line segment **Center of Dilation**, **scale factor** is

**Dilation preserves the angle of measure**.

Note that the **pre-image** and the **image** are **parallel**.

Observe that the points (center of dilation **collinear**.

And, the points (C, B and B') are also **collinear**.

**congruent corresponding angles.**

Also, from

Move (4 x 3 = 12 units) up on the y-axis, and (2 x 3 = 6 units) left on the x-axis tor reach the end-point of

Similarly,

from

From

New **end-points:**

Find the length of **distance formula**:

Hope this solution is helpful.