A right triangle in the first quadrant has the coordinate axes as sides, and the hypotenuse passes through the point (1, 8). Find the vertices of the triangle such that the length of the hypotenuse is minimum

A house and a barn are on the same side of a driveway.  Two walkways are planned to connect the buildings to a point P on the driveway.  On a grid, the house would be at (5, 2), the barn would be at (-1, 4), and the driveway would be located along the x-axis.  Where should point P be located to make the length of the walkways as short as possible?  a (0,0)  b (-1, -4)  c (5, -2)  d (3, 0)

A rectangle is fenced off for a robot competition. The dimensions of the competition area are 35 feet by 25 feet. To help track the robots, the southwest vertex of the rectangle is assigned coordinates (0,0) and the northeast vertex is assigned coordinates (35, 25). Show Your Work The robot that traveled the farthest distance began at (3,18) and moved in a linear path for 5 seconds. After 5 seconds, the robot's position was at (31, 6). The robot traveled approximately feet after 5 seconds. Round your answer to the nearest tenth. The approcimate average speed of the winning robot is feet per second.

Find the equation of the circle