Graph AFGH with vertices F(-2, 2), G(-2,-4) and H(-4,- 4) and its image after the similarity transformation. Dilation: (x, y) - ( ) Reflection: in the x-axis Polygon 6 Undo - Redo x Reset 5- 4- 3- 2- 1- -5 -4 -3 -1 4. -1 -2 -4
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- Sketch the image of the rectangle with vertices at (0, 0), (1, 0), (1, 2), and (0, 2) under the specified transformation.T is a reflection in the line y = x.Sketch the image of the triangle with vertices (0, 0), (1, 0), and (0, 1) under the specified transformation.T is a reflection in the x-axis.A pre-image of a figure contains the point (3, 4). Distinguish the location of this point in the image of the transformation (x, y) → (y, x) by plotting your original point and your transformed point on a coordinate plane.
- The parts (a) and (b) of this problem are independentof each other.G1 G24 51 236sx yt u v(a) Prove that the graphs G1 and G2 are isomorphic byexhibiting an isomorphism from one to the other byconcrete arguments and verify it by using adjacencymatrices. Please take the ordering of the vertices as1, 2, 3, 4, 5, 6 while forming AG1, adjacency matrix ofG1.Warning: One must stick to the labelings ofthe vertices as they are given, if one changesthe labelings/orderings etc., the solution willnot be taken into account.(b) Consider the complete graph K13 with vertex setV13 = {u1, u2, u3, · · · , u13}.Let H = (V, E) be the simple graph obtained fromK13 by adding a new vertex u, i.e. V = V13 ∪ {u}and deleting the edges {u1, u2} and {u2, u3} andadding the edges {u1, u} and {u, u2} and keepingthe remaining edges same.Determine whether H has an Euler circuit or not,an Euler path or not. One must validate any conclusion by clear arguments.Suppose a linear transformation: T:R2-->R2 is formed by taking a rotation counterclockwise of 180 degrees, followed by a reflection across the x2-axis. Describe the points that will be moved back to their original position by this transformation.Find the coordinates of the vertices of the figure after the given transformation.
- Sketch the image of the rectangle with vertices at (0, 0), (1, 0), (1, 2), and (0, 2) under the specified transformation.T is the expansion represented by T(x, y) = (2x, y).Describe the reflection of △FGH△FGH with vertices F(−3, 2), G(−4, −1)F(-3, 2), G(-4, -1), and H(−6, −1)H(-6, -1), to its image △F′G′H△F′G′H′ with vertices F′(2, −3), G′(−1, −4)F′(2, -3), G′(-1, -4), and H′(−1, −6)H′(-1, -6). Use decimals, if necessary. (x, y) ----- I don't know how to represent reflecctions as coordinates.A pre-image of a figure contains the point (10, 3). Distinguish the location of this point in the image of the transformation (x, y) -> (x - 11, y+ 6) by plotting your original point and your transformed point on a coordinate plane.
- The ABC Toy Company is creating two similar pieces for a board game, as shown below. How could the toy maker confirm that the pieces are similar using the definition of similarity in terms of similarity transformations? triangles GHI and JKL Verify ∠G ≅ ∠J and ∠I ≅ ∠L by reflection. Verify segment GH ≅ segment JK and segment GI ≅ segment JL by reflection. Verify ∠G ≅ ∠J and ∠I ≅ ∠L by translation. Verify segment GH ≅ segment JK and segment GI ≅ segment JL by translation.Describe the reflection of △FGH△FGH with vertices F(−3, 2), G(−4, −1)F(-3, 2), G(-4, -1), and H(−6, −1)H(-6, -1), to its image △F′G′H△F′G′H′ with vertices F′(2, −3), G′(−1, −4)F′(2, -3), G′(-1, -4), and H′(−1, −6)H′(-1, -6). Use decimals, if necessary. (x, y) → ( , ) ---- I don't know how to put it into coordinates.Sketch the image of a unit square [a square with vertices at (0, 0), (1, 0), (1, 1), and (0, 1)] under the specified transformation. T is a reflection in the line y = −x.