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Form 4 Matrices and Transformations Questions and Answers

Matrices and Transformations Questions and Video Answers. Several questions have been answered. All answers are in video format.

Lessons (20)

• 1.    The point (5, 2) undergoes the transformation #((3,2),(-1,0))#followed by a translation #((-6), (11))# Determine the coordinates of the image.
  2m 38s

• 2.    The image of a point A, under the transformation represented by the matrix T = #((1,-1),(0,2))# is A' (-2, 4). Find the coordinates of A.
  2m 38s

• 3.    A point P’ (x’, y’) is the image of a point P(x, y) under a transformation T, given by the matrix #((3, 4),(4,-3))#. a) Express x’ and y’ in terms of x and y. b) If a point Q and its image Q’ under the transformation T lie on the same line y=mx, find two possible values of m.
  6m 19s

• 4.    A transformation is represented by the matrix #((1,2),(3,2))#. This transformation maps a triangle ABC of the area #3 cm^2# on to another the area of triangle
  3m 43s

• 5.    Determine the matrix of transformation that represents the following transformations: Reflection in x + y = 0, followed by a positive quarter turn about (0, 0).
  10m 24s

• 6.    Points A (2, 2) and B (4, 3) mapped onto A’ (2, 8) and B’ (4, 15) respectively by a transformation T. Find the matrix of T.
  6m 12s

• 7.    The area of triangle FGH is #21cm^2#. The triangle FGH is transformed using the matrix #((4, 5),(1,2))#. Calculate the area of the image of triangle FGH.
  2m 28s

• 8.    In a transformation, an object with an area of #5 cm^2# is mapped onto an image whose area is #30 cm^2# image. Given that the matrix of the transformation is #((x, x-1),(2,4))#, find the value of x.
  2m 44s

• 9.    The area of a triangle is 24 square units. The triangle is mapped onto image P by the matrix #((6,5),(3,4))#. Find the area of the image P.
  1m 53s

• 10.    Under a transformation #((4,-3), (2,3))#, triangle OAB is mapped onto triangle O’A’B’ with vertices O(0,0), A’(18,0) and B’(18,6). Find the area of triangle OAB.
  4m 28s

• 11.    A triangle T whose vertices are A (2, 3), B (5, 3) and C (4, 1) is mapped onto triangle #T_1# whose vertices are #A_1# (4, 3), #B_1# (-1, 3) and #C_1# (x, y) by a transformation M = #((a,b),(c,d))#. a) Find the: (i) Matrix M of the transformation. (ii) Coordinates of C1. b) Triangle T2 is the image of triangle T1 under the reflection in the line y = x. find a single matrix that maps T onto T2.
  14m 52s

• 12.    The vertices of a triangle T are A(1,2), B(4,2) and C(3,4). The vertices of triangle T’, the image of T are A’#(1/2 , 1)#, B’(2,1) and C’#(3/2 ,2)#. Determine the transformation matrix M = #((a,b),(c,d))# that maps T onto T’.
  6m 41s

• 13.    The vertices of a triangle PQR are P(3,2), Q(0,-1) and R(2,1). A transformation matrix M, maps triangle PQR onto triangle P’Q’R’ whose vertices are P’(-7,2), Q’(2,-1) and R’(4,-1). Find M-1, the transformation that maps P’Q’R’ onto PQR.
  8m 10s

• 14.    The vertices of a triangle ABC are A (-1, -4), B (3, 3), C (2, 5). Find the image of the triangle under the transformation whose matrix is #((4,-2),(6,-3))#. Draw the triangle and its image on the same axis.
  6m 39s

• 15.    A parallelogram whose vertices are A (1, 0), B (3, 0), C (4, 2) and D (2, 2) is mapped onto a parallelogram A’B’C’D’ by a transformation whose matrix is M. Under the transformation, the images of A and C are A’ (0, 1) and C’ (-2, 4) respectively. i. Find the matrix M ii. Plot the parallelogram ABCD and its image on the given grid. iii. A’B’C’D’ is mapped onto ABCD by a transformation T. Obtain
  9m 52s

• 16.    A rectangle OABC has the vertices O (0’ 0), A (2, 0), B (2, 3) and C (0, 3). O’A’B’C is the image of OABC under the translation given by#((0),(4))#. O”A”B”C” is the image of O’A’B’C’ under the transformation given by the matrix #((0,-1),(1,0))#. Draw the rectangles OABC, O’A’B’C’ and O”A”B”C” on the grid provided. Use your diagram to find the centre of rotation which maps OABC onto O”A”B”C”.
  17m 58s

• 17.    A transformation #T_1# maps the triangle ABC whose coordinates are A (-2, 0), B (1, -2), C (0, 1) onto triangle ABC whose coordinates are A’ (, ), B’ (, 1) and C’ (1, ) Another transformation #T2# maps the same triangle ABC onto triangle A''B''C'' whose coordinates are A'' (4,2 ), B'' (1,4 ), C (2, 1). a). On the same axes, plot triangle ABC, A’B’C’ and ABC b) Determine i. #T_1# ii. #T_2#
  17m 58s

• 18.    On the grid provided, ABCD is a trapezium. (NB: coordinates of the figure are A (2, 0), B (6, 0), C (6, 5) and D (2, 2)) a) ABCD is mapped positive quarter turn. Draw the image A'B'C'D' on the grid b) A transformation #((-2,-1),(1,-1))# maps A'B'C'D' to A''B''C''D'' (i) Obtain the coordinates of A''B''C''D'' (ii) Plot the image A''B''C''D'' on the grid
  18m 57s

• 19.    The figure on the grid shows a triangular shaped object ABC and its image A’B’C’ a) (i) Describe fully the transformation that maps ABC onto A’B’C’. (ii) Find a 2 x 2 matrix that transforms triangle ABC onto triangle A’B’C’. b) The matrix P = #(( 2,1),(1, 1))# transforms triangle ABC onto A”B”C”. (i) Find the coordinates of A”, B” and C”. (ii) Draw the image A”B”C”.
  14m 20s

• 20.    A quadrilateral ABCD has vertices A (4, -4), B (2, -4), C (6, -6), D (4, 2). a) On the grid provided, draw the quadrilateral ABCD. b) A'B'C'D' image of ABCD under positive quarter turn about the origin. On the same grid, draw the A'B'C'D' c) A"B"C"D" is the image of A'B'C'D' under the transformation given by the matrix#((1,-2),(0,1))#
  15m 49s