Coordinate plane

On the coordinate plane (6, 2) and (0, 6) are the endpoints of the diagonal of a square. What is the distance between point (0, 0) and the closest vertex of the square?

The slope of the diagonal is 4/-6, which reduces to -2/3. So the midpoint of this diagonal is (3,4). This is the point at which both diagonals will meet.
The slope of a perpendicular line will be the negative reciprocal, so 3/2. So that will be the slope of the other diagonal, which intersects this midpoint and the other two points of the square.
So the point of the square closest to the (0,0) mark will be at (1,1).

Then we can use the Pythagorean theorem to calculate the distance as $$\sqrt{2}$$