Let R₀ = [0, 1] × [0, 1] be the unit square. The translate of a map Φ₀(u, v) = (ϕ(u, v), ψ(u, v)) is a map

Sketch the parallelogram P with vertices (1, 1), (2, 4), (3, 6), (4, 9) and find the translate of a linear mapping that maps R₀ to P.

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D(u, v) = (a + d(u, v), b + y(u, v)) where a, b are constants. Observe that the map Do in Figure 15 maps Ro to the parallelogram Po and that the translate maps Ro to P. V Ro Ro (4, 5) (2, 2) P D (u, v) = (2+4u + 2v, 1 + u + 3v) Go(u, v) = (4u+ 2v, u + 3v) G(u, v) = (2+4u +2v, 1+u+3v) -U (6, 3) -X (1,4). (-1, 1). (2, 3) (6,4) Po (4,4) (4,1) P3 P (2, 1) (8,5) (6,2) (3, 2)