A is a point on the y-axis whose ordinate is 5 and B = (-3, 1). Find AB.

The coordinates of point A on the y-axis, whose ordinate is 5, are (0, 5).

Distance between 2 points (x₁, y₁) and (x₂, y₂) = $\sqrt{(x$2 - x1)^2 + (y2 - y1)^2}

Distance between A(0, 5) and B(-3, 1) =

$= \sqrt{(-3 - 0)^2 + (1 - 5)^2}\\[1em] = \sqrt{(-3)^2 + (-4)^2}\\[1em] = \sqrt{9 + 16}\\[1em] = \sqrt{25}\\[1em] = 5$

Hence, the distance between A(0, 5) and B(-3, 1) is 5 units.