In this exercise, we use Figure 42 to prove Herons principle of Example 7 without calculus. By

Question:

In this exercise, we use Figure 42 to prove Heron’s principle of Example 7 without calculus. By definition, C is the reflection of B across the line MN (so that BC is perpendicular to MN and BN = CN). Let P be the intersection of AC and MN. Use geometry to justify the following:

= 0. (a)   and NC are congruent and  (b) The paths APB and APC have equal length. (c) Similarly, AQB and AQC

A h1 M 0 Q P 01 0 N . |h 5 1 C

Example 7

EXAMPLE 7 Show that if P is the point for which the path APB in Figure 9 has minimal length, then 0. =

A hi 0 X 0 L L-X B h

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For  book-img-for-question

Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

Question Posted: