Question

In: Math

:Geometric transformations Determine the coordinates of the images of the vertices A(2,1), B(3,2), C(2,3) of a...

:Geometric transformations

Determine the coordinates of the images of the vertices A(2,1), B(3,2), C(2,3) of a triangle t, following the composition of two transformations:
1. a homothety with centre C1(0,0) and ratio
k = 5, followed by a 2. rotation with centre C2(6,-1) and angle = 30°

Steps of the resolution that must be part of the answer:

1. Construct and order in a matrix product the sequence of matrices corresponding to this succession of transformations (expressed in exact values = fractions and reduced square roots ).

2. Calculate the global transformation matrix Tg (expressed in exact values).

3. Determine the coordinates of the image of the triangle ABC by this succession of transformations ( expressed in exact values AND in decimal numbers rounded to two decimal places).

4. Draw the geometrical construction corresponding to these two transformations applied to the ABC triangle.


kindly solve it conceptually and clearly by diagram and explaining it's all parts

Solutions

Expert Solution


Related Solutions

Find the coordinates of the images of A (2,3) and B (-2,3) under the following transformations....
Find the coordinates of the images of A (2,3) and B (-2,3) under the following transformations. Assume that all dilations are centered at the origin. Draw sketches to justify your answer. a. A dilation with a scale factor of 3 followed by a dilation with a scale factor 2. b. A dilation with scale factor 2 followed by a translation with a slide arrow from (2,1) to (3,4). c. A translation with a slide arrow from (2,1) to (3,4) followed...
w x y z a 3,2 4,1 2,3 0,4 b 4,4 2,5 1,2 0,4 c 1,3...
w x y z a 3,2 4,1 2,3 0,4 b 4,4 2,5 1,2 0,4 c 1,3 3,1 3,1 4,2 d 5,1 3,1 2,3 1,4 a) for this game, use iterated elimination of strictly dominated strategies. explain each step of your work. b) what strategy profiles survive IESDS? what are the Nash equilibrium of this game?
Consider the following stage game Strategy L R T (3,2) (1,5) B (2,1) (1,1) It is...
Consider the following stage game Strategy L R T (3,2) (1,5) B (2,1) (1,1) It is repeated over two periods. The payoffs of the players over the two periods is the sum of the payoffs over the two periods. Is there a subgame perfect equilibrium of the repeated game in which (T,L) is played in period 1? If so, describe the equilibrium. If not, explain why not.
Find the coordinates of the orthocenter of the triangle whose vertices are A(3, 1), B(0, 4) and C(-3, 1).
Find the coordinates of the orthocenter of the triangle whose vertices are A(3, 1), B(0, 4) and C(-3, 1).
Find the area of △ABC. Where:A=(3,2), B=(2,4), C=(0,2) Suppose that a×b=〈−1,1,−1〉〉 and a⋅b=−4 Assume that θ...
Find the area of △ABC. Where:A=(3,2), B=(2,4), C=(0,2) Suppose that a×b=〈−1,1,−1〉〉 and a⋅b=−4 Assume that θ is the angle between aand b. Find: tanθ= θ= Find a nonzero vector orthogonal to both a=〈5,1,5〉, and b=〈2,−4,−1〉 Find a nonzero vector orthogonal to the plane through the points: A=(0,2,2), B=(−3,−2,2), C=(−3,2,3). Find a nonzero vector orthogonal to the plane through the points: A=(0,1,−1), B=(0,6,−5), C=(4,−3,−4)..
Consider the tetrahedron with vertices A= (0;1;1); B= (4;0;1); C=(2;1;3), and D= (2;2;0). a) What is...
Consider the tetrahedron with vertices A= (0;1;1); B= (4;0;1); C=(2;1;3), and D= (2;2;0). a) What is the area of the parallelogram spanned by vector AB and vector AD? b) Determine the angle between the two vectors AB and CD. c) Find an equation of plane through vector BC and point D.
8). 2 charges, 12.33 µC each, are located at two vertices B & C of an...
8). 2 charges, 12.33 µC each, are located at two vertices B & C of an equilateral triangle ABC with sides 2 cm each. Another charge q is located at point A. Calculate q in micro Coulomb so that net POTENTIAL at the mid point of BC will be ZERO. 9). Three charges, + 22 uC, - 22 uC and + 22 uC are placed at A (0,5cm), B (5cm,0), C(-5cm,0). Calculate the potential energy of the whole system of...
Determine an A-B-C classification for these items: • Which items are A, B, and C -...
Determine an A-B-C classification for these items: • Which items are A, B, and C - explain how you derive the answers? Item   Unit Cost Annual volume(000) 1 300 25 2 90 30 3 30 60 4 50 10 5 15 70 6 100 40 7 10 60 Hint: Determine the Annual Dollar Value (Unit Cost * Annual Volume) for each item and the sum of the individual Annual Dollar Values. Arrange the items in descending order based on Annual...
The reward for bearing risk is called the: a. geometric return b. average return c. real...
The reward for bearing risk is called the: a. geometric return b. average return c. real return d. risk premium e. total retum .
Sketch images of the folloing, shading the described regions. (a)|z|<4(b) |z − i| < 2 (c)...
Sketch images of the folloing, shading the described regions. (a)|z|<4(b) |z − i| < 2 (c) 1 <|z − i + 2| < 2 (d) Re(z) <|z|
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT