Mathematica's interactive graphics capabilities let you determine the coordinates of a single point. You can also get arbitrary sequences of points and paths, and analyze and manipulate the coordinate lists like any other data in Mathematica.
In the Drawing Tools palette, choose the Get Coordinates tool:
When you hover over a graphic, the coordinates of the point under the cursor are displayed next to the cursor. Clicking a point marks the point in the graphic for later copying. Similarly, dragging marks a set of points along the path:
To mark a rectangular area on a plot, do Alt+Drag on Windows or Option+Drag on Macintosh. You can resize a marked area using the resize handles. Clicking and dragging on a side of a rectangle will move it without resizing.