Final answer:
The distance between A(3a, 3b) and B(a, b) is 2sqrt(a^2 + b^2).
Step-by-step explanation:
To find the distance between points A(3a, 3b) and B(a, b), we can use the distance formula which is derived from the Pythagorean theorem. The distance formula is: d = sqrt((x2 - x1)^2 + (y2 - y1)^2). In this case, the coordinates of point A are (3a, 3b), and the coordinates of point B are (a, b). Plugging these values into the formula, we get: d = sqrt((a - 3a)^2 + (b - 3b)^2) = sqrt((-2a)^2 + (-2b)^2) = sqrt(4a^2 + 4b^2) = 2sqrt(a^2 + b^2). Therefore, the distance between A(3a, 3b) and B(a, b) is 2sqrt(a^2 + b^2).