WeBWorK Standalone Renderer

(a) Find an affine change of coordinates that takes the unit square with vertices

$P^* = (0,0), \ Q^* = (1,0), \ R^* = (0,1), \ S^* = (1,1)$
in the $uv$ -plane to the rectangle with vertices

$P = \left(-3,1\right), \ Q = \left(0,1\right), \ R = \left(-3,6\right), \ S = \left(0,6\right)$
in the $xy$ -plane.

$x = x(u,v) =$
$y = y(u,v) =$

(b) Find the absolute value of the determinant of the Jacobian for this change of coordinates.

$\displaystyle \left| \frac{\partial(x,y)}{\partial(u,v)} \right| = \bigg| \mathrm{det}$

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$			$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$

$\bigg| =$

You can earn partial credit on this problem.