Length of a line segment.

The question: List all the points that have whole-number coordinates and are

a) 5 units from the origin

b) 10 units from the origin

for a, since its 5 units I used the line segement formula, l^2=[(x2-x1)^2]+[(y2-y1)^2], and set 25 equal to the formula, but I got 25=(x2)^2 + (y2)^2.

To find the whole number coordinates is it trial and error or is there some way to find the values of x2 and y2 that would give whole number coordinates.

Re: Length of a line segment.

Quote:

Originally Posted by

**darksoulzero** The question: List all the points that have whole-number coordinates and are

a) 5 units from the origin

b) 10 units from the origin

For a) Are all of these such points $\displaystyle (\pm 5,0)~\&~(0,\pm 5)~?$

Is it true that $\displaystyle [\pm 3]^2+[\pm 4]^2=25~?$

Are there any others?