Distances and missing coordinates

The horizontal and vertical changes form perpendicular sides of a right triangle, so AB2=(x_2-x_1)2+(y_2-y_1)2. Take the non-negative square root for the length. Find changes, square, add, then root. For a missing coordinate, square the given distance, isolate the coordinate square, retain both roots, and only then apply any location condition. From (1,2) to (4,6), the length is sqrt(32+42)=5. Points (t,2) at distance 3 from (1,2) have t=1+-3. Check: lengths cannot be negative. A negative change is squared; it is not a negative contribution to the squared distance.