Question

Triangle ABC is to be dilated through point P with a scale factor of 3. How many units away from point A along ray Ray P A will A’ be located?


Triangle A B C. Side A C has a length of 3, A B is 4, C B is 5. Point A is 5 units away from point P, the center of dilation.



units

Answer 1

To determine how many units away from point A the dilated point A' will be located along ray PA, we can apply the concept of dilation.

In a dilation with a center of dilation at point P and a scale factor of k, the distance from the center of dilation to the dilated point (A') is given by the formula:

\[
\text{Distance from P to A'} = k \times \text{Distance from P to A}
\]

In this case, the scale factor \(k = 3\) and the distance from point P to point A is given as 5 units. Therefore, we compute the distance from P to A' as follows:

\[
\text{Distance from P to A'} = 3 \times 5 = 15 \text{ units}
\]

Now, to find the distance from point A to point A', we subtract the distance from P to A from the distance from P to A':

\[
\text{Distance from A to A'} = \text{Distance from P to A'} - \text{Distance from P to A} = 15 - 5 = 10 \text{ units}
\]

Thus, point A' will be located 10 units away from point A along ray PA.

The answer is **10 units**.