Question

A dilation with center C and scale factor k maps B onto D. Find k if CD=5 and CB=10

Answer 1

A dilation with center C and scale factor k maps B onto D. Find k if CD=5 and CB=10

Solution:

The definition of dilation is next:

Each point B put in correspondence point D such that $\overrightarrow{CB} = k\overrightarrow{CD}$.

Then we have

$$\left| \overrightarrow {C B} \right| = | k | \cdot \left| \overrightarrow {C D} \right|,$$ $$10 = | k | \cdot 5,$$ $$| k | = \frac {5}{10},$$ $$| k | = \frac {1}{2},$$ $$k = \frac {1}{2} \text{ or } k = - \frac {1}{2}.$$

Answer:

$$k = \frac {1}{2} \quad \text{or} \quad k = - \frac {1}{2}.$$