Using Midpoint and Distance Formulas

Let's begin with graphing the segment $\overline{KM}$ on a coordinate plane.

We want to find point $Q$ so that the ratio between $KQ$ and $KM$ is $\frac{2}{5}.$ $\dfrac{KQ}{KM} =\dfrac{2}{5}$ To make this happen, we should place $Q$ so that it lies on the segment and is $\frac{2}{5}$ of the way from $K$ to $M.$ Notice that we can divide the segment $\overline{KM}$ into $5$ equal segments as shown below.

Therefore, $\frac{2}{5}$ of this distance is like moving along the segment by $2$ of these squares.

We can tell that the coordinates of the point $Q$ are $(1,1).$