1\( R_1 \) is the reflection in the x-axis and \( R_2 \) is the reflection in the y-axis. Which single transformation is \( R_1 \mathbin{o} R_2 \)? Choose from: rotation [(0, 0), -90°], rotation [(0, 0), 90°], rotation [(0, 0), 180°], rotation [(0, 0), 270°].
2\( R_1 \) is the reflection in the x-axis and \( R_2 \) is the reflection in the y-axis. What is the image of A(2, 3) under \( R_1 \mathbin{o} R_2 \)? Choose from: A'(2, -3), A'(-2, 3), A'(-2, -3), A'(3, 2).
3\( r_1 \) and \( r_2 \) are the rotations [(0, 0), 45°] and [(0, 0), 45°] in the same direction. What is the image of M(1, 2) under \( r_1 \mathbin{o} r_2 \)? Choose from: A'(-2, 1), A'(1, 2), A'(-1, 2), A'(2, 1).
4Which transformation is given by the combined transformation of reflections in the lines x = 3 and x = 5? Choose from: translation by \( \begin{pmatrix} 2 \\ 0 \end{pmatrix} \), rotation through +180°, rotation through +90°, translation by \( \begin{pmatrix} 4 \\ 0 \end{pmatrix} \).
5What is the combined transformation \( R_1 \mathbin{o} R_2 \) of the rotations \( R_1[(0, 0), \theta] \) and \( R_2[(0, 0), \alpha] \)? Choose from: \( [(0, 0), \theta - \alpha] \), \( [(0, 0), \theta + \alpha] \), \( [(0, 0), \theta \times \alpha] \), \( [(0, 0), \theta \times \frac{1}{\alpha}] \).
6If \( T_1 = \begin{pmatrix} m_1 \\ n_1 \end{pmatrix} \) and \( T_2 = \begin{pmatrix} m_2 \\ n_2 \end{pmatrix} \), what is \( T_2 \mathbin{o} T_1 \)? Choose from the difference, the sum, the product of matching parts, and the cross product of the parts.
7What is the combined transformation \( E_1 \mathbin{o} E_2 \) of the enlargements \( E_1[(a, b), K_1] \) and \( E_2[(a, b), K_2] \)? Choose a scale factor from: \( K_1 + K_2 \), \( K_1 - K_2 \), \( K_1 \times K_2 \), \( K_1 \times \frac{1}{K_2} \).
8Triangle ABC has vertices A(2, 2), B(6, 2) and C(2, 5). It is reflected first in the X-axis and then in the Y-axis. Find the coordinates of the image under the combined transformation, name the combined transformation, and show the object and the image on one graph.
9Triangle ABC with vertices A(1, 2), B(4, -1) and C(2, 5) is reflected first in the line x = -3 and then in the line y = 4. Find the image triangle A''B''C'' and show it with triangle ABC on one graph.
10Triangle ABC with vertices A(1, 2), B(4, -1) and C(2, 5) is reflected in the line \( r_1 \) (x = 4) and then in the line \( r_2 \) (x = -1). Find the combined transformation \( R_2 \mathbin{o} R_1 \), and show the image A'B'C' and triangle ABC on one graph.
11Triangle ABC has vertices A(4, 0), B(3, 3) and C(1, -1). It is rotated through 90° about the origin and then through 180° about the origin in the same direction. Which single transformation is this? Find the image A'B'C' and show both triangles on one graph.
12Triangle PQR has vertices P(1, 2), Q(4, -1) and R(2, 5). It is rotated through -90° about the origin and then through -180° about the origin. Which single transformation is this? Find the image and show both triangles on one graph.
13\( R_1 \) is the rotation through 90° about the origin and \( R_2 \) is the rotation through -270° about the origin. What is \( R_2 \mathbin{o} R_1 \)? Use it to transform the quadrilateral with vertices A(-4, 0), B(-6, 2), C(-4, 3) and D(2, 5), and show the object and image on one graph.
14Quadrilateral ABCD has vertices A(3, 0), B(4, 2), C(2, 3) and D(1, 2). It is rotated through +180° about the origin, and the image is then rotated through 90° about the origin in the positive direction. Find the image A''B''C''D'' and show both quadrilaterals on one graph.
15P(2, 1), Q(-1, 4) and R(-2, 2) are the vertices of triangle PQR, and \( T_1 = \begin{pmatrix} 2 \\ -3 \end{pmatrix} \) and \( T_2 = \begin{pmatrix} 3 \\ 2 \end{pmatrix} \) are two translation vectors. Using \( T_1 \mathbin{o} T_2 \) or \( T_2 \mathbin{o} T_1 \), find the image of triangle PQR and show PQR and P'Q'R' on one graph.
16Triangle BUN has vertices B(5, 3), U(1, 4) and N(2, 1), and the translation vectors are \( T_1 = \begin{pmatrix} -3 \\ -2 \end{pmatrix} \) and \( T_2 = \begin{pmatrix} -1 \\ -4 \end{pmatrix} \). Find \( T_1 \mathbin{o} T_2 \), use \( T_2 \mathbin{o} T_1 \) to find the image of triangle BUN, and show BUN and B'U'N' on one graph.
17The line segment PQ has P(-3, 5) and Q(7, -4). \( E_1[(0, 0), 2] \) and \( E_2[(0, 0), \tfrac{3}{2}] \) are two enlargements, and PQ is transformed by \( E_1 \mathbin{o} E_2 \). Find the centre and scale factor of the combined enlargement, find the image P'Q', and show PQ and P'Q' on one graph.
18Triangle ABC has vertices A(2, 3), B(4, 5) and C(6, 2), and the enlargements are \( E_1[(0, 0), 4] \) and \( E_2[(0, 0), \tfrac{1}{2}] \). Find the scale factor of \( E_2 \mathbin{o} E_1 \), then use it to find the image A'B'C' and show both triangles on one graph.
19If \( R_1[(0, 0), \theta_1] \) and \( R_2[(0, 0), -\theta_2] \) are two rotations, what are the centre and the angle of the combined rotation \( R_2 \mathbin{o} R_1 \)?
20Why does changing the order of two reflections in parallel lines change the final image, while changing the order of two translations does not?
21The point K(3, 1) is reflected in the X-axis and then in the line y = x. Which single transformation does this? Find the image of K.
22The point W(4, -4) is reflected in the line y = -2 and then in the line y = 1. Find the combined translation and the image of W.