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

Answer:
Point A' will be located 10 units away from point A along ray PA
Step-by-step explanation:
we have
The scale factor is 3
step 1
Find out the distance PA'
we know that
The distance PA' is equal to multiply the distance PA by the scale factor
so
[tex]PA'=PA*3[/tex]
we have
[tex]PA=5\ units[/tex]
substitute the given values
[tex]PA'=(5)*3=15\ units[/tex]
step 2
Find out how many units away from point A along ray PA will A’ be located
we know that
[tex]PA'=PA+AA'[/tex]
we have
[tex]PA=5\ units[/tex]
[tex]PA'=15\ units[/tex]
substitute the given values and solve for AA'
[tex]15=5+AA'[/tex]
[tex]AA'=15-5=10\ units[/tex]
therefore
Point A' will be located 10 units away from point A along ray PA