- #1

- 748

- 8

## Homework Statement

So imagine 4 rigid rods connected together to form a dashed quadrilateral as shown in the picture.

Now AB is fixed, can not be changed in anyway, while all other sides (AD, BC and CD) are connected but can move freely. The initial conditions (dashed quadrilateral) are given.

Now we rescale the dashed BC and AD sides to given values. Note that the length of CD remains constant!

Find coordinates of points C and D of newely generated quadrilateral in such way that the slope of AD and BC is minimally changed.

## Homework Equations

## The Attempt at a Solution

Ok so the way I see the problem I have 4 values to determine

$$(x_C, y_C)\text{ and } (x_D, y_D).$$

First 3 (out of 4) equations are

$$ ||\vec{BC}|| = \sqrt{(x_C - x_B)^2 + (y_C - y_B)^2}$$

$$ ||\vec{AD}|| = \sqrt{(x_D - x_A)^2 + (y_D - y_A)^2}$$

$$ ||\vec{DC}|| = \sqrt{(x_C - x_D)^2 + (y_C - y_D)^2}$$

The forth one is the one I am struggling with. I know that the slope equals ##\tan \varphi = \frac{\Delta x}{\Delta y}## but I'm not really sure what to do with that. I'm quite sure I need to find the relation between ##\vartheta## and ##\varphi## first.

EDIT: This probably doesn't lead to a linear system of equations. I assume Lagrangian multiplier will be needed or some other method for finding multivariate extremes. I will kindly ask the moderators to change the topic title.

#### Attachments

Last edited by a moderator: