Question

find the distance between the points (a,-2) and (3a,5)

Answer 1

To find the distance between two points $A = (A_x, A_y),\ B = (B_x, B_y)$ you may use the formula

$\overline{AB} = \sqrt{(A_x-B_x)^2+(A_y-B_y)^2}$

In your case, the formula becomes

$\overline{AB} = \sqrt{(a-3a)^2+(-2-5)^2} = \sqrt{(-2a)^2+(-7)^2} = \sqrt{4a^2+49}$