1The point A(4, 2) is reflected in the line y = x, and its image A'(2, 4) is rotated through +90° about the origin. Which single transformation does this combined transformation represent? Choose from: reflection in the X-axis, reflection in the Y-axis, reflection in the line y = x, reflection in the line y = -x.
2P(x, y) is reflected in the Y-axis to P'(-x, y), and P' is rotated through +90° about (0, 0) to give the final image P''(-y, -x). Which single transformation does this combined transformation represent? Choose from: reflection in the X-axis, reflection in the Y-axis, reflection in the line y = x, reflection in the line y = -x.
3The point A(4, -1) is first reflected in the line y = x. The image A' is then given a half turn about the origin. Which is the final image A''? Choose from: A''(-1, 4), A''(-1, -4), A''(1, -4), A''(1, 4).
4The point B(3, 2) is first enlarged by E[(1, 2), -2], and the image is then translated by \( T = \begin{pmatrix} 1 \\ 2 \end{pmatrix} \). Which is the final image B''? Choose from: B''(-2, 4), B''(-2, 3), B''(2, -4), B''(-3, 2).
5ΔABC has vertices A(2, -1), B(2, 1) and C(4, -1). It is first reflected in the line y - x = 0, and the image is then given a half turn about the origin. Find the final image ΔA''B''C'' and show it with ΔABC on one graph.
6ΔBIN has vertices B(1, 2), I(-1, -2) and N(5, 0). It is translated by \( T = \begin{pmatrix} 1 \\ 2 \end{pmatrix} \), and the image is reflected in the X-axis. Write the coordinates of the vertices of both images and show ΔBIN and its images on one graph.
7ΔMAN has vertices M(-1, 2), A(2, 1) and N(1, 0). Find its image under translation by \( T = \begin{pmatrix} 1 \\ 2 \end{pmatrix} \). Reflect that image in the line x = -2, and show ΔMAN and ΔM''A''N'' on one graph.
8T is a translation and R is a rotation. ΔABC with A(2, 1), B(2, 4) and C(5, 2) is translated by \( \overrightarrow{AB} \) and then rotated through 90° in the positive direction about the origin. Find the image under the combined transformation RoT, and show ΔABC and its image on one graph.
9ΔABC with vertices A(1, 4), B(4, 1) and C(7, 5) is translated by \( \overrightarrow{AC} \) and then rotated through 90° in the negative direction about the origin. T is the translation and R the rotation. Find the image under RoT and show ΔABC and its image on one graph.
10Triangle XYZ has vertices X(2, 3), Y(2, 6) and Z(3, 4). It is translated by \( \begin{pmatrix} -2 \\ 3 \end{pmatrix} \), and the image is enlarged by E[(0, 0), 2]. Write the coordinates of the vertices of the images and show them on one graph.
11ΔMNP has vertices M(1, 1), N(3, 1) and P(2, 3). Find its image under a rotation of 90° in the positive direction about the origin. Enlarge that image with centre (-1, 2) and scale factor 2. Show the final image ΔM''N''P'' and ΔMNP on one graph.
12E is the enlargement with centre (3, 1) and scale factor 2, and R is the reflection in y = x. ΔABC has vertices A(2, 3), B(4, 5) and C(1, -2). Find its image under the combined transformation EoR and show both figures on one graph.
13\( G_1 \) is the enlargement with centre (3, 4) and scale factor 2, and \( G_2 \) is the reflection in the line y = x. ΔPQR has vertices P(-3, 5), Q(7, 4) and R(6, -2). It is transformed by \( G_2 \) o \( G_1 \) to give ΔP'Q'R'. Find P', Q' and R', and show both figures on one graph.
14Triangle CUT has vertices C(2, 5), U(-1, 3) and T(4, 1). It is rotated through 90° in the negative direction about the origin and then enlarged by E[(0, 0), 2]. Find the coordinates of the images and show the object and images on one graph.
15A parallelogram GITA has vertices G(2, 2), I(6, 2), T(7, 4) and A(3, 4). It is rotated through 90° in the positive direction about the origin and then enlarged by E[(0, 0), 3]. Find the coordinates of the images and show the object and images on one graph.
16Triangle BAT has vertices B(4, 6), A(2, 2) and T(8, 2). It is rotated through 90° in the positive direction about the point P(1, 3) and then reflected in the X-axis. Find the coordinates of the images and show the object and images on one graph.
17A parallelogram DUCK has vertices D(2, 3), U(1, 1), C(4, 1) and K(5, 3). It is rotated through 90° in the positive direction about the point A(4, 0) and then reflected in the line x = y. Find the coordinates of the images and show the object and images on one graph.
18Explain the difference between GoF and FoG, using A(4, 2), a reflection in y = x and a rotation of +90° about the origin.
19A point P(x, y) is given a half turn about the origin and the image is reflected in the X-axis. Find the single equivalent transformation.
20Triangle ABC with A(1, 0), B(2, 1) and C(3, -1) is translated by (1, 2) and then reflected in x = 2. Write one rule for the whole combined transformation and use it to find C''.