.. Please help me here
1. Matrices and Transformations 1 . a) (i) On the grid provided, with the same scale on both axes, draw the square S whose vertices are (0, 0), (2, 0), (2,2) and (0, 2). (1 mk) (ii) Find the coordinates and draw the image T of S under the transformation whose matrix A maps a point (x, y) onto (x', y) (3 mks) (iii) Draw the image U of S under the transformation whose matrix is (2 mks) (b) (i) Find the product AB and draw the image V of S under the transformation whose matrix is AB (3 mks) (ii) Describe the single transformation that maps S onto V (1 mk) 2. On the grid provided, draw triangle POR with P(2,3), Q(1,2) and R(4,1). On the same axes draw triangle P"Q"R" with vertices P"(-2,3), Q"(-1,2) and R"(-4, 1). (2mks) (a) Describe fully a single transformation which will map triangle POR onto triangle Plo"R". (1mk) (b) On the same plane, draw triangle P'Q'R' the image of triangle POR under reflection in the line y = -x. (2mks) (c) Describe fully a single transformation which maps triangle P'Q'R' onto triangle Plo"R". (2mks) (d) Draw triangle P." Q''R' such that it can be mapped onto triangle POR by a position quarter about (0,0) (2mks) (e) State all pairs of triangles that are oppositely congruent. (1mk) 3. a) Given the transformation matrices " = (1 2 ) and and that transformation Ti followed by Ta can be replaced by a single transformation T, write down the matrix for T. (3 marks) a) Find the inverse of matrix T (2 marks) b) The points A" (7,-11), B"(-7,-13), C"(-8,16) and D"(8,8) are the images of points A, B, C and D respectively under transformation T, followed by T2 Write down the co-ordinates of A, B, C, and D. (5 marks) 4. A(3, 7), B(5, 5), C(3, 1), D(1, 5)4. A(3, 7), B(5, 5), C(3, 1), D(1, 5) a) On the grid provided in the next page, plot ABCD on a Cartesian plane (2mks) b) A'B'C'D' is the image of ABCD under a translation -9 . Plot A'B'C'D' and state its coordinates. (2mks) c) Plot A"B"C"D", the image of A'B'C'D' after a rotation about (-1, 0) through a positive quarter turn. State its coordinates. (3mks) d) A"B"C"D" is the image of A"B"C"D" after a reflection in the line y=x + 2. Plot A"B"C"D" and state its coordinates (3 mks) 5. A transformation represented by the matrix | , maps P(0.0), Q(2,0), R(2,3) and S(0,3) onto P', Q', R', S' a) On the grid provided draw the quadrilateral PQRS and P'Q'R'S' (4mks) b) (i) Determine the area of PQRS (1mk) (ii) Hence or otherwise find the area of P'Q'R'S' (2mks) C) A transformation represented by the matrix _ maps PQ'R'S' onto P"Q"R"S". Determine the matrix of transformation that would map P"Q"R"S" onto PQRS (3mks) 6. A translator T maps P (8, -2) onto P (-2, -3). Find the image of Q (6, -2) under the same translation. (3 mks) 7. The vertices of a triangle are A(2,5), B(4,3) and C(2,3). H represents a half turn rotation about the point (0,2). ) Draw triangle ABC and A, B, C under H (4 marks) b) T represents a reflection in the lone x= 0 and K represent a translation ( 2 ). Find the coordinates of A , B ,C" of A, B,C under TK. Hence draw A", B', C (4 marks) c) Describe a single transformation that maps ABC onto A", B',C" (2 marks) 8. Given triangle ABC with vertices A (-6, 5), B(-4, 1) and C(3, 2) and that A(-6, 5) is mapped onto A'(-6, -4) by a shear with y-axis in variant. On the grid provided below; (i) draw triangle ABC (ii) draw triangle A'B'C , the image of triangle ABC, under the shear (iii) determine the matrix representing the shear (b) Triangle A'B'C is mapped onto A"B"C" by a transformation defined by the matrix/ 3/2 (i) Draw triangle A'B'C" on the same grid as ABC and A'B'C (ii) Describe fully a single transformation that maps All Blloll9. (a) Under a certain rotation A( 2,0) is mapped onto A'(-4, 2) and B(0,5) is mapped onto B'(-9, o) (i) On the grid provided plot the lines AB and A'B'Cn the same axes (ii) Hence determine by construction the co-ordinates of the centre and angle of rotation (b) Under a quarter positive turn about the origin O, A' is mapped onto A" and B' is mapped onto B". Determine the co-ordinates of A" and Bll (c) Describe fully a single transformation which would map A to A" and B to B" 10. A transformation T is represented by the matrix 0 -1) and transformation fo -1 0 1 dby the matrix. Given that a rectangle has co-ordinates at A (1,2) B(6, 2), C(6, 4) and D (1, 4) and that under T the image of ABCD is A B, C, D and under U the image of A, B,C,D is A,BC,D2: (a) Find the co-ordinates of ABC, D, and AB,C2D2 (b) On the grid provided, plot ABCD, A BiCID, and ABCD2 (c) Describe the transformation represented by:- () U (ii) UT (d) If ABCDz were to be transformed by a transformation represented by the matrix to map onto AiBjCabs . What would be the area of ABC;D3 11. The vertices of a quadrilateral are A(2,2) B(8,2) , C (8,6) and D(6,4) under a rotation the images of vertices A and D are A(0,8) and DI(-2, 12). (a) On the grid provided and using the same axes draw the quadrilateral ABCD and the points A' and D' (b) Determine the centre and angle of rotation (c)Locate the points B' and C' under the rotation and complete the quadrilateral 12. A translation maps the point P(5, -3) onto P (2, -5) (a) Determine the translation vector T (b) A Point R' is the image of R(-2, -3) under the same translation in (a) above, find the magnitude of P R' 13. Triangle ABC has vertices at A(0, -1), B(4, 3)and C(2,2). (a) Find the coordinates of image triangle A'B'C' of triangle ABC under translation vector (b) Given that triangle A'B'C" is the image of triangle A'B'C' under an enlargement scale factor 3, centre O(0,0) , find the coordinates of A", B" and Cl (c) If the area of triangle A'B'C' is 24 cm , calculate the area of triangle A "B"cl! (d) Find the m male ABC
