A region R in the xy-plane is given. Find equations for a transformation T that maps a rectangular region S in the uv-plane onto R, where the sides of S are parallel to the u- and v-axes as shown in the figure below. (Enter your answers as a comma-separated list of equations.)
R is bounded by y = 2x − 4, y = 2x + 4, y = 4 − x, y = 6 − x

Question

A region R in the xy-plane is given. Find equations for a transformation T that maps a rectangular region S in the uv-plane onto R, where the sides of S are parallel to the u- and v-axes as shown in the figure below. (Enter your answers as a comma-separated list of equations.)
R is bounded by y = 2x − 4, y = 2x + 4, y = 4 − x, y = 6 − x

likeabossssssss · Answer

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what do u think it is ?

holsteremission · Answer

Original region:
|dw:1478878997456:dw|
Rewrite the equations for each line in standard form:
$$\begin{cases}y=2x+4\y=2x-4\y=6-x\y=4-x\end{cases}\implies\begin{cases}-2x+y=4\-2x+y=-4\x+y=6\x+y=4\end{cases}$$
Since the lines bounding the region are parallel, an easy choice for $u$ and $v$ would be $u=-2x+y$ and $v=x+y$. Then the region $S$ in the $uv$ plane is a rectangle with $-4\le u\le4$ and $4\le v\le 6$.