Hello, jarny!

A right triangle is formed in the first quadrant by the x and y axes

and a line through the point (1,2).

a) Write the length L of the hypotenuse as a function of x.

Code:| (0,b)* | * | * (1,2) | o | * | * - - + - - - - - * - - | (a,0)

The line with intercepts 0,b)" alt="(a,0),\0,b)" /> has the equation: .

Since is on this line: .

The length of the hypotenuse is given by: .

Substitute [1] into [2]: .

Therefore: .