3. Part B. Jim is confused now because he knows that he learned that rigid transformations preserve distance. Yet, he says that he can see that the distances AC and BD in the completed figure are not the same! Explain the error in Jim's thinking. Write your answer in the space provided. BI
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- A transformation that preserves length and angle measure is: A) a rigid motion B) a non-rigid motion C) a corresponding figure D) a pre-imageQuadrilateral HIJKHIJK has vertices H(−1, 3)H(−1, 3), I(2, 3)I(2, 3), J(2,−1)J(2,−1), and K(−3,−1)K(−3,−1). It is dilated by a scale factor of 77 with a center of dilation at (0, 0)(0, 0). Part A. What are the coordinates of the image H′I′J′K′H′I′J′K′? Part B. What is the algebraic representation of the dilation? Enter the correct coordinates in the boxes.Draw the image of the figure under the given transformation. Then describe the transformation as a rigid motion or not a rigid motion. Justify your answer.
- Quadrilateral HIJKHIJK has vertices H(−1, 3)H(−1, 3), I(2, 3)I(2, 3), J(2,−1)J(2,−1), and K(−3,−1)K(−3,−1). It is dilated by a scale factor of 77 with a center of dilation at (0, 0)(0, 0). What are the coordinates of the image H′I′J′K′H′I′J′K′?Triangle ABC has vertices with coordinates of A 1, 9 , B 1,12 , and C 7, 9 .(a) Draw ABC on the given grid.(b) Transform ABC into A'B'C' by switchingthe x and y coordinates of each point. Insymbolic form:(x,y), (y,x)A 1, 9 ______________ B 1,12 ______________ C 7, 9 ______________ (c) Is this transformation a rigid motion? Explain. Use tracing paper if necessary.Isosceles trapezoid RSTU, with K as midpoint of RS, Las midpoint of ST , M as midpoint of TU , and N as midpoint of RU , is shown. Point P is the intersection of KM and NL. RK S P M Which transformation carries the trapezoid onto itself? O A. a 90* rotation clockwise about P O B. a 180° rotation clockwise about P O c. a reflection over KM D. a reflection over NL
- Triangle ABC goes through a series of three transformations, resulting in triangle A'B'C'. The three transformations are listed below.• a rotation 180° clockwise about the origin• a reflection over the x axis• a reflection over the y axisTriangle ABC has vertex A located at (2,-3). Using the coordinates of this point, explain how the threetransformations map vertex A onto vertex. A'.Explain your answer.Trying to go ABC is reflected across the X axis and then across the Y access which rotation is equivalent to this composition transformations transformationsDirection: Refer to the given worded problem below and answer the question provided. A man is suspended from a bungee rope and moving according to the equation. Where h(t) feet is directed distance of the weight from its equilibrium position at tseconds, and the positive distance means above its equilibrium position. 1. At what time is the displacement of theMan 5 feet below its equilibrium positionfor the first time?
- LINEAR ALGEBRA Linear transformations are useful in computer graphics and can be used to rotate or translate figures in two-dimensional space.Begin with a triangle with vertices: A (0,0), B (1,0), and C (0,1)a) Sketch and give the coordinates of the new triangle, after transformation T1: a reflection of the original triangle in the x-axis.b) Sketch and give the coordinates of the new triangle, after transformation T2: a rotation of the original triangle around the origin of ? = 135 degreesc) Sketch and give the coordinates of the new triangle, after transformation T3: an expansion of the original triangle represented by ?3(x, y) = (3x, y)d) Sketch and give the coordinates of the new triangle, after transformation T4: the shear of the original triangle represented by ?4(x, y) = (x, y + 4x)Directions: The picture below shows a double right circular cone indicating its parts. Suppose a plane is to intersect and cut the cone. a. Draw a figure that will be creates when the plane is to cut the cone horizontally and perpendicular to the axis. b. Draw a figure when the plane is tilted and intersects only one cone forming a bounded curve.Exercise 3. Read Example 3 (p. 739). Explain how the geometric meaning of the cross product helps solve this example.We won’t be covering the last two subsections, but they might be worth taking a look at. The subsection “Torque” (p. 739 – 740) covers a physical application of the cross product. While the last subsection “Triple or Box Product” (p. 740 – 741) goes over a geometric way that the dot product and cross product interact with each other.