Calculate the distance between A(5, -3) and B on the y-axis whose ordinate is 9.

We know that any point on the y-axis has co-ordinates of the form (0, y).

The ordinate of point B is 9.

So, the point B is (0, 9).

Distance between the given points = $\sqrt{(x$2 - x1)^2 + (y2 - y1)^2}

Distance between A(5, -3) and B(0, 9):

$= \sqrt{(0 - 5)^2 + (9 - (-3))^2}\\[1em] = \sqrt{(-5)^2 + 12^2}\\[1em] = \sqrt{25 + 144}\\[1em] = \sqrt{169}\\[1em] = 13$

Hence, the distance between A(5, -3) and B(0, 9) is 13 units.