Answer:
15
Explanation:
There are a couple of ways to go at this. 1) find the distance AB and multiply by 3. 2) find the coordinates of A' and B', then find the distance A'B'.
It helps if you're familiar with the "Pythagorean triple" (3, 4, 5).
Finding the distance between two points
The formula for the distance between two points makes use of the relationship given by the Pythagorean theorem. The difference of x-coordinates is considered as one leg of a right triangle, and the difference of y-coordinates is considered as the other leg. Then the hypotenuse is the straight-line distance between the points. The Pythagorean theorem gives the relationship:
... (straight-line distance)² = (x-coordinate difference)² + (y-coordinate difference)²
For your points, this is
... AB² = (7-3)² + (5-2)² = 16 +9 = 25
... AB = √25 = 5
You will notice that the x-difference is 4, the y-difference is 3, so the lengths form the triple (3, 4, 5) when the smallest is listed first. This triple of triangle lengths is used often in algebra problems (and occasionally in real-life), so is worth remembering.
Effect of dilation
The scale factor of 3 affects all coordinates and distances. It will multiply every coordinate by 3, so that the image points are A'(9, 6) and B'(21, 15). Of course, this multiplies the differences between coordinates by 3, and so multiplies the distance AB by 3. That is,
... ║A'B'║ = 3×║AB║ = 3×5 = 15