Transformation Review 2

\[ \definecolor{ucrblue}{rgb}{0.0627,0.3843,0.6039} \definecolor{ucrgold}{rgb}{0.9686,0.6941,0.2824} \definecolor{ucrred}{rgb}{0.8941,0,0.1686} \definecolor{ucrgreen}{rgb}{0.4706,0.7451,0.1255} \definecolor{ucraccent}{rgb}{1.0000,0.9569,0.8392} \DeclareMathOperator*{\LO}{O} \DeclareMathOperator*{\Lo}{o} \DeclareMathOperator*{\Recip}{Recip} \DeclareMathOperator*{\abs}{abs} \DeclareMathOperator{\pow}{pow} \]

Notes

You can reference these sections to review.

• Chapter 2.1: Vectors and Translation
• Chapter 2.2: Scaling Vectors and Subsets of the Plane
• Chapter 2.3: Movement along Lines
• Chapter 2.4: Orthogonality and Reflection
• Chapter 2.5: Inverse Functions
• Chapter 2.6: Describing Rotation in Cartesian Coordinates
• Chapter 2.7: Rotations
• Chapter 2.8: Involution

Knowledge Checks

1. A particle travels at constant velocity on the time intervals \([0,6]\) and \((6,12]\). It is at \((2,1)\) at time \(4\), at \((-1,3)\) at \(6\), and \((5,4)\) at time \(12\). Write an equation that describes the position of the particle at time \(t\) and determine the position of the particle at time \(0\).
2. A particle rotates counterclockwise around the point \((3,2)\) at constant speed of \(4\). It is at the point \((6,2)\) at time \(0\). Write an equation that models the position of the particle at time \(t\).
3. Take \(A\) to be a particle that moves on the line segment with endpoints \((1,2)\) and \((5,7)\). It is at \((1,2)\) at time \(0\) and it moves along the line segment at a speed of \(2\). Take \(B\) to be a particle that rotates around \(A\) in a counterclockwise direction as \(A\) travels. It is a distance of \(3\) to the right of \(A\) at time \(0\) and has a speed of \(14\).
   1. Write down equations that model the motion for \(A\) and \(B\).
   2. Determine how long it takes for \(A\) to reach \((5,7)\).
   3. Determine how many full orbits \(B\) has made by the time \(A\) reaches \((5,7)\).
4. A rectangle \(R\) has vertices at \((2,3)\), \((3,5)\), \((-1,7)\), and \((-2,5)\). Determine a rigid transformation so that the vertex of \(R\) at \((2,3)\) is at \((0,0)\) and the edge \(\overline{(2,3)(3,5)}\) is on the \(x\)-axis. Then determine the positions of vertices after applying this transformation. \end{enumerate}

• Knowledge Checks PDF
• Knowledge Checks Solutions

Remember, do the knowledge checks before checking the solutions.

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