1If the man at A(1, 2) walks 6 units to the left and then 4 units down, what are the coordinates of the point A' he reaches?
2Which of these transformations is a translation: turning a figure; moving a figure from one place to another; making a figure larger; forming the image of a figure in a mirror?
3When a triangle is translated by a vector, what happens to its shape and area: only the shape changes; only the area changes; both change; or both stay the same?
4Which formula gives the image of P(x, y) under the translation vector \( T = \begin{pmatrix} a \\ b \end{pmatrix} \): \( P'(x + a, y + b) \), \( P'(x - a, y - b) \), \( P'(x - a, y + b) \) or \( P'(x + a, y - b) \)?
5Which is the image Q' of Q(-2, 4) under \( T = \begin{pmatrix} 3 \\ 2 \end{pmatrix} \): \( Q'(-1, 6) \), \( Q'(1, 6) \), \( Q'(-1, -6) \) or \( Q'(5, 6) \)?
6The point P(3, -4) is translated to P'(-2, -1). What is the translation vector T: \( \begin{pmatrix} 1 \\ -3 \end{pmatrix} \), \( \begin{pmatrix} 5 \\ -5 \end{pmatrix} \), \( \begin{pmatrix} -5 \\ 3 \end{pmatrix} \) or \( \begin{pmatrix} -1 \\ -3 \end{pmatrix} \)?
7P(-1, 4) is translated 5 units to the right along the x-axis. What is its image: P'(4, 4), P'(-6, 4), P'(-1, 9) or P'(4, -4)?
8A point (x, y) is translated by (-3, 5). Which point is obtained: (x - 3, y - 5), (x + 3, y + 5), (x - 3, y + 5) or (x + 3, y - 5)?
9Translate each of the three shapes by the vector a drawn beside it: triangle ABC, parallelogram MNOP and pentagon PQRST.
10What is meant by translation? Write with an example.
11Find the images of A(-1, 3), B(2, -2), C(5, 6), D(-4, -4), E(7, 2) and F(2, -4) under the translation vector \( T = \begin{pmatrix} 2 \\ -2 \end{pmatrix} \).
12Triangle PQR with vertices P(2, 3), Q(-2, 4) and R(4, -2) is translated to triangle P'Q'R' by \( T = \begin{pmatrix} 3 \\ 2 \end{pmatrix} \). Find the vertices of P'Q'R'.
13For the points A(3, 5), B(-3, 5) and C(3, -5): to which point does \( \overrightarrow{AB} \) translate A? To which point does \( \overrightarrow{BC} \) translate B? To which point does \( \overrightarrow{CA} \) translate C?
14A translation vector moves A(-5, 6) to A'(-3, 3). Find the translation vector.
15Find the vector that translates R(4, 7) to R'(-3, -5). To which point does this vector translate S(4, 1)?
16If U(5, 3) is translated to U'(4, 2) by \( T = \begin{pmatrix} a \\ b \end{pmatrix} \), find a and b. To which point does T translate V(-5, 4)?
17Triangle ABC has vertices A(1, -1), B(-2, 2) and C(3, 3). Find the vertices of its image A'B'C' under \( T = \begin{pmatrix} 2 \\ 3 \end{pmatrix} \), and draw both triangles on a graph.
18A(1, 8), B(-3, 9), C(0, 13) and D(4, 12) are the vertices of parallelogram ABCD. Find \( \overrightarrow{AB} \). Then translate ABCD by \( \overrightarrow{AB} \), write the vertices of the image and draw both parallelograms on a graph.
19A(-4, 6), B(3, -2) and C(1, 2) are the vertices of triangle ABC. The vector \( T_1 = \begin{pmatrix} 1 \\ -2 \end{pmatrix} \) translates ABC to A'B'C', and then \( T_2 = \begin{pmatrix} -2 \\ 3 \end{pmatrix} \) translates A'B'C' to A''B''C''. Find the vertices of A'B'C' and A''B''C'', and draw all three triangles on one graph.
20A point P(x, y) is reflected in the line x = 1, and that image is reflected again in the line x = 3. Compare the final image with the image of P(x, y) under the translation vector T(4, 0). What conclusion can be drawn?
21A point is translated by \( T = \begin{pmatrix} -4 \\ 5 \end{pmatrix} \) and its image is (1, 2). Find the original point.
22What is the image of the origin O(0, 0) under \( T = \begin{pmatrix} a \\ b \end{pmatrix} \)? What does this tell you?
23Why is a triangle and its image under a translation always congruent?
24Write the translation vector for a move of 3 units left and 7 units up, and find the image of (2, -5) under it.