1. Under a translation, a point A(3, 7) is mapped at the point A'(-1, 3). What will be the translation vector? Where will the point (7, 0) be mapped by the same translation?
2. A triangle with vertices A(1, 2), B(4, -1), and C(2, 5) is reflected successively in the lines x = 5. Find by stating coordinates and graphically represent the images under these transformations.
3. A(1, 0), B(1, 4) and C(-1, 4) are the vertices of ∆ABC. It is rotated by 90° clockwise about the origin. Find the vertices of image of the triangle and plot the ∆ABC and ∆A'B'C' on the same graph.
4. Enlarge the ∆ABC having the vertices A(3, 4), B(-2, 6) and C(1, -5) with the centre (1, 2) and scale factor of -2 so that the ∆A'B'C' which is the image of ∆ABC is formed. Find the coordinates of A', B' and C'. Also present the ∆ABC and ∆A'B'C' on the same graph paper.
5. If a point A (2, 0) is translated to A’ (0, 3) by a translation vector
6. If a point A (5, 2) is translated to A’ (12, 9) by a translation vector
7. If the image of A (2, a) and B (4, b) under the translation vector
8. If the image of A (a, 5) and B (4, b) under the translation vector
9. If a point P (2, 5) is translated to the point P’ (2, 3), find the translation vector and the image of Q (4, 0) under the same translation vector.
10. The vertices of triangle NPA are N (2, 1),
P (4, - 4) and A (0, -2). Find the co-ordinates of the image of triangle NPA under the translation
(x, y) ⟶ (x +3, y + 4).
11. Under an enlargement centre (0, 0) and scale factor 4, a point A (b, a) is mapped to the point A’ (6, -8). Find the values of a and b.
12. An enlargement E [(a, b), 2] maps the point A (4, 1) to the point A’ (6, 1). Find the centre (a, b) of the enlargement.
13. Two end points of a line segment AB are
A (2, 3) and B (4, 5). Find the image of AB when reflected in X-axis.
14. In each of the following condition find the image of A(2, 7):
i. When reflected the line x = y
ii. When reflected the line x = 2
15. The co-ordinates of P and Q are (2, 0) and (0, 3) respectively. Find the image of Q under the reflection in an axis which makes point P invariant.ii. When reflected the line x = 2
16. The co-ordinates of P and Q are (0, 5) and (6, 8) respectively. Find the image of Q under the reflection in an axis which makes point P invariant.
17. Under a reflection, A (1, 3) and B (a, b) are mapped to A’ (3, 1) and B’ (5, 2). Find the axis of reflection and the co-ordinates of B.
18. In the line segment AB, A (2, 3) and B (4, 5). Find the image of AB when rotated about the origin by +90°.
19. In the line segment AB, A (2, 3) and B (4, 5). Find the image of AB when rotated about the origin by -90°.
20. In the line segment AB, A (2, 3) and B (4, 5). Find the image of AB when rotated about the origin by -270°.
21. The image of points A (4, 5) and B (6, 3) are A’ (-5, 4) and B’ (a, b) under a rotation. Find the values of a and b.
22. Under a certain reflection, the image of points A (4, 3) and B (a, 8) are A’ (3, 4) and B’ (b, 2 – 2a). Find the values of a and b.
23. The vertices of ∆ABC are A(1, 4) ,B (2, 5) and C (7, 4). Find the co- ordinates of image of ∆ABC under the translation by the translation vector
24. The co- ordinates of a triangle are A (1, 4), B(2, 8) and C (6, 3). The translation vector T is define by T (x, y) = (x + 3,y + 5). Find the co - ordinates of all the image using the translation vector and show in a graph.
25. The vertices of quadrilateral PQRS are P (2, 3), Q(4, 5), R (6, 2) and S(7, 5). If the image of P is P' (6, 8) under a translation. Find the co- ordinates of all the images under the translation vector.
26. A (2, 1), B (4, 5) and C (-1, 4) are the vertices of the ∆ABC. Find the co- ordinates of the vertices of the image ∆'AB'C' of ∆ABC when it is enlarged with origin as centre and a scale factor of 2. Draw the ∆ABC and ∆A'B'C' on the same graph paper.
27. Enlarge the ∆ABC having the vertices A( 3, 4) , B (-2, 6) and C (1, -5) with the centre (1, 2) and scale factor of -2 so that the ∆A'B'C' which is the images of ∆ABC is formed. Find the co- ordinates of A', B', and C' . Also present the ∆ABC and ∆A'B'C' on the same graph paper.
28. Enlarge the ∆ PQR having the vertices P(3, 4), Q(1, 1) and R (4, 1) with the centre (1,-1) and a scale factor -2 so that ∆ P'Q'R' which is the image of ∆ PQR is formed. Find the co- ordinates of P', Q' and R'. Also present the ∆ PQR and ∆ P'Q'R' on the same graph paper.
29. Enlarge the ∆ ABC having the vertices A (3, -1) , B(1, -3) and C (5, -3) with the centre (1, 1) and a scale factor 2, so that the image ∆A'B'C' of the ∆ABC is formed. Find the co- ordinates of A',B' and C'. Also present both the triangles on the same graph paper.
30. On a graph paper draw the ∆ PQR, whose vertices are P (6, 1) Q (6, 5) and R (8, 5). If the ∆ PQR maps to ∆ P'Q'R' by and enlargement about the center (2, 3) with scale factor of 1/2; find the co- ordinates of P',Q' and R'. Show this image ∆ P'Q'R' on the same graph paper.
31. On a graph paper, draw the ∆ ABC whose vertices are A (3, 2), B(4, 2) and C (3, 4). On the same graph paper draw the ∆A'B'C', the image of ∆ ABC by an enlargement, with the vertices A' (6, -1), B' (4, -1) and C'(6, -5). Find it centre of enlargement and the scale factor.
32. If ∆ ABC with vertices A (-4, 0) B (-1, 1) and C (-2, -3) is mapped into ∆ A'B'C ' by an enlargement with centre P(0, 1) and the co- ordinates of B' is (1, 1). Find the co- ordinates of A' and C' and draw ∆ ABC and ∆ A'B'C' on the same graph.
33. Determine the vertices of the image ∆ A'B'C' formed when the ∆ABC with vertices A (2, 8) , B (8, 6) and C(4, 2) is reflected on the line y – 4 = 0. Also draw both triangles on the same graph paper.
34. If A' (6, 3) , B' (4, 5) and C" (2, 2) are the images of the points A, B and C of ∆ ABC under reflection in the line x - 4 = 0, determine the co- ordinates of the ∆ ABC. Also draw ∆ ABC and ∆ A'B'C' on the same graph paper.
35. Determine the vertices of the image ∆ A'B'C' formed when ∆ ABC with vertices A(1, 3) , B(4, 5) and C (6, 2) is reflected in the line x + 2 = 0. Also draw both triangles on the same graph paper.
36. Points A (4, 3), B (6, 4), C (5, 6) and D (3, 5) are the vertices of a square ABCD. The square ABCD is reflected about the line through (0, 0) and (-2, 2). Find the vertices of image of the square ABCD and present both the figures on the same graph.
37. If the vertices of ∆ MNP are M (1, 1) , N (3, 1) and P (2, 3). Plot the image of ∆ MNP under the rotation through 90° in anti- clockwise direction about the origin. Then determine the co- ordinates of the corresponding vertices.
38. A (1, 0), B (1, 4) and C (-1, 4) are the vertices of ∆ ABC and it is rotated 90° clockwise about the origin. Find the vertices of image of the triangle and plot the ∆ ABC and ∆ A' B' C' on the same graph paper.
39. If A' (-1, -3), B'(2, -4) and C' (3, 4) are the image points of A, B and C of triangle ABC under rotation about (0, 0) through +90°. Determine the co-ordinates of the triangle ABC. Also draw the triangles ABC and A'B' C' on the same graph paper.
40. The vertices of ∆ ABC are A (2, 3), B (4, 5) and C (6, 2). Plot the image of ∆ ABC under the rotation through 90° in anticlockwise direction about the origin. Then determine the co- ordinates of the corresponding vertices.