# Minimizing the Area of a Triangle

- Author:
- Tim Brzezinski

- Topic:
- Area

**Suppose a segment is drawn in the first quadrant of the coordinate plane and has variable slope.**

**Suppose this segment passes through the point (2,3).**This line also has an

**x-intercept of (c,0)**and a

**y-intercept of (0,d)**, where c, d > 0. Use calculus to algebraically determine the slope of this line for which the

**area of the displayed right triangle is minimum.**Then use calculus to

*prove*this area is indeed the minimum area.

**How does your result compare with what this applet suggests? Note: The red point is moveable.**

**Note to Instructors/Students:**

**The purple point is moveable too, should you wish to solve a problem with similar context.**