Point M is located at (-2, 7). If point N is 13 units away from point M, how many possible coordinate pairs (x, y) could point N have? Explain what you can determine about the values of x and y.

Answer 1

If the domain of x is real numbers, for any given point (x,y), there are an infinite number of values for x between x and x-13. If the domain of x is integers, there are a finite number of values for x. This means that, in most cases, there will be an infinite number of y values if the domain of x is real and the function doesn't map to a horizontal line.

Try drawing on a sheet of graph paper some sample points 13 units from point (-2,7). What shape does this represent? Is there an equation to map from x to y coordinates for this shape?