Using the homogencous coordinate transformation matrix, rotate the triangle ABC with A (2, 3), B (5, 5), and C (4, 3) by an angle of 45 degree about the point (1, 1). Also draw the diagram of each step.

Using the homogencous coordinate transformation matrix, rotate the triangle ABC with A (2, 3), B (5, 5), and C (4, 3) by an angle of 45 degree about the point (1, 1). Also draw the diagram of each step.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.CR: Review Exercises

Problem 29CR: Use the standard matrix for counterclockwise rotation in R2 to rotate the triangle with vertices...

See similar textbooks

Related questions

Q: Which option describes the linear transformation represented by the matrix ? preserves orientation…

A: Check for all the options and choose the correct one.

Q: Assume that T is a linear transformation. Find the standard matrix of T. T: R?→R? first reflects…

A: Linear transformation Firstly we need to write the linear transformation and then from their we…

Q: Give a geometric description of the linear transformation defined by the matrix product.

A: Given that:

Q: : Two points, A and B, constituting a portion of a two-dimensional shape are moved to points C and…

A: Given: The coordinates of the points given in the statement are, A(2,1),B(5,3),C(5,2),D(7,2+33) The…

Q: Using the homogeneous coordinate transformation matrix, rotate the triangle (2, 3), B (5, 5), and C…

Q: What is transformation matrix for reflecting over the y-axis? a. b. C. d. e.

Q: Give a geometric description of the linear transformation defined by the matrix product.

Q: 2. Describe the geometry of the linear transformation represented by each matrix. Explain. 3 0 a. ^=…

A: Follow the steps.

Q: Assume that T is a linear transformation. Find the standard matrix of T. T: R→R? first reflects…

A: Given that, T is a linear transformation. and we have to find the standard matrix of T. And also…

Q: 1 v = (Km Cs+ Vmax)²

A: Let L be a linear transformation. Apply L to the given relation we get, Lv=L1KmCs+Vmax2 We can use…

Q: T-M₂R)→R² Find the linear transformation whose matrix ~ = [ ²2 Мор=

A: A linear transformation is given by, T:M2×2ℝ→ℝ2 where MT= 1 0-1 1 2-1 1-1. The objective…

Q: v - (-9, 2) is transformed using the transformation matrix A = What is the resulting vector? Show…

Q: Match each coordinate rule to a description of its transformation. (x, y)--> (x + 3, y) [Choose] (x,…

A: To match: The following coordinate rule to description of its transformation: Calculation: The…

Q: Find the 3x3 matrix that produces the described composite 2D transformation below, using homogeneous…

A: Find the 3×3 matrices that produce the described composite 2D transformations, using homogeneous…

Q: Match each coordinate rule to a description of its transformation. (x.y)--> (x+3, y) [ Choose )…

A: When a point is shifted three units rights, the x coordinate increases by 3. So for the first…

Q: Which representation of a transformation on a coordinate grid does NOT preserve congruency? B (x,y)…

A: which option on a coordinate grid does not preserve congruency.

Q: Find the composite transformation matrix for the following transformation sequence. And also find…

Q: The transformation with matrix T, where T= 3 1 , maps the point (x, y) onto the point 4 3 (x', y'),…

Q: R2 → R3 first performs horizontal shear that transforms e2 into e2 - 2 e1 and then reflects points…

Q: Assume that T is a linear transformation. Find the standard matrix of T. T: R→R first reflects…

A: T is a linear transformation. T:ℝ2→ℝ2 first reflects point through the origin and then reflects…

Q: the angle of rotation for the matrix transformation 2 2

A: Given the matrix of transformation is f(xy)=32-121232xy To find the angle of rotation.

Q: Find the 4 by 4 transformation matrix for the figure below form the dotted line position to the…

Q: Let T : R? → R² be the linear transformation that projects vectors onto the line y = -x and then…

Q: Obtain the compliance matrix for the following transformation of the coordinates.

Q: a) Find the matrix of the linear transformation, 1 -3 x1 F( x2 ) + x2 -1 + x3 -2 = x1 4 -2 X3 b)…

Q: Explain how to determine whether a function T : V → W is a linear transformation. Secondly give some…

A: We have to explain how to determine whether a function T:V→W is a linear transformation then…

Q: Let f(z) = (az + b)/(cz + d) and ad – bc # 0. If this transformation maps zo → Wo, 1→ W1 and Z2 → W2…

A: Given , f(z)=(az+b)(cz+d) , ad-bc≠0. This transformation maps z0→w0, z1→w1 and z2→w2 Taking…

Q: Find the global transformation matrix to transfer the local coordinate system (x1, y1, z1) to the…

A: Given :- The global transformation matrix to transfer the local coordinate system x1 , y1 , z1 to…

Q: Solve the problem. Let T: 2->2 be a linear transformation that maps u = Use the fact that T is…

A: Given , T(u)=(7,-8) i.e. T(4,5)=(7,-8) And T(v)=(7,-4) i.e. T(2,-1)=(7,-4) Now ,we have find image…

Q: Let f be the linear transformation represented by the matrix 2 -2 A = (2) 3 -2 Find the point (x, y)…

A: Given, A=2-23-2 Need to find the point x,y such that fx,y=-4,-1.

Q: Q2: Determine the Transformation matrix that transfer the shown object to its final destination…

A: Given a circle at the starting point 6,-1 and the ending point 5,4.5. The translation matrix is…

Q: Determine whether or not the following linear transformation is invertible, and justify your answer

Q: Please explain how you know the transformation is linear or not! Thank you! Which of the following…

Q: Define Transformation? Write down the properties of Linear transformation and rotational…

A: In mathematics, a transformation is a function f (usually with some geometrical underpinning) that…

Q: Please describe using text keyboard (NOT HANDWRITING), what is meant by “The Kernel,” and “The…

A: Kernal:- Let T: V - U be a linear transformation. The Kernal of T, denoted by Ker T or N(T) and is…

Q: You need to rotate point bP1=n [10 10 0] 60 degrees on the X axis and 10 units on the Z axis. Write…

Q: R?. Find the matrix transformation TA which describes the reflection on the line y = 2x in . G Give…

A: To find: The matrix transformation TA that describes the reflection on R2 by the line y=2x. Consider…

Q: Give one application of linear transformation then explain while including illustrations for support

A: linear transformation has many application but image rotate and flip is one of application

Q: Determine the 2 x 2 matrix that represents the reflection along the line y = -V3x. Use this matrix…

A: As per the question first we have to construct the transformation matrix which reflects any point on…

Q: Find the 3×3 matrix that produces the described composite 2D transformation below, using…

A: According to the given information it is required to construct the 3×3 matrix that produces the…

Q: 3. (1 point) Let f : R² → R³ be the linear transformation determined by (;)-() (1)-() 3 4 -6 (1)…

Q: Let 3. 3. be de tined by the linear transformation X - 49 3x find the of matrix the base of opace…

Q: Find the change-of-coordinates matrix from B to C. Find [x]c for x = - 2b, +4b2. Use part (a). %3D

A: Transition matrix

Q: 5. What is a linear transformation? Explain what it means for a matrix A to represent a linear…

Q: Find the 3 x3 matrix that produces the described composite 20 transformation below, using…

Q: Find the standard matrix of a linear transformation T: R° → R° given by the formula - (E)-L T -3x1…

A: Here we have to find the standard matrix of a linear transformation .

Q: 5. Let A be the linear transformation R2 R2 that first reflects vectors across the line y=z, then…

A: see my solution

Q: Show the Horizontal shear transformation for geometric figures by a 2x2 matrix ?

Q: c). Find the standard matrix for the compositions of three linear transformations defined by a…

A: Here given a rotation of 30° about y-axis, followed by a reflection about xz-plane, followed by a…

Q: Give a geometric description of the linear transformation defined by the matrix product.

A: Given: The matrix product as:…

Question

I need the answer as soon as possible

So-Compter Grathics
( Using the homogencous coordinate transformation matrix, rotate the triangle ABC with A
(2, 3), B (5, 5), and C (4, 3) by an angle of 45 degree about the point (1, 1). Also draw the
diagram of each step.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Use the standard matrix for counterclockwise rotation in R2 to rotate the triangle with vertices (3,5), (5,3) and (3,0) counterclockwise 90 about the origin. Graph the triangles.
Explain what it means in terms of an inverse for a matrix to have a 0 determinant.
Show that the matrix below does not have an LU factorization. A=0110
Referring to Exercise 19, suppose that the unit cost of distributing the products to stores is the same for each product but varies by warehouse because of the distances involved. It costs $0.75 to distribute one unit from warehouse 1 and $1.00 to distribute one unit from warehouse 2. Organize these costs into a matrix C and then use matrix multiplication to compute the total cost of distributing each product.