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 - 2, y = 2x + 2, y = 2 - x, y = 4 - x.

Question

Mathematics

Manuel Graves

29 September, 02:57

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 - 2, y = 2x + 2, y = 2 - x, y = 4 - x.

+4

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Dylan Short · Answer 1

Y = 2x - 2 → 2x - y = 2

y = 2x + 2 → 2x - y = - 2

y = 2 - x → x + y = 2

y = 4 - x → x + y = 4

Set u = 2x - y and v = x + y. Thus, we obtain the following bounds: - 2 ≤ u ≤ 2 and 2 ≤ v ≤ 4, which resembles the rectangle in uv-plane