SEE OPT Maths: Transformation Using Matrix

1. Which transformation does the matrix 

-1001     represent? Find it. 

2. Which transformation does the matrix 

  0 -1-1   0represent? Using the matrix, find the image of the point A(6, -2).
 

3. Find the transformation matrix which represents the reflection on the line y = -x. 

4. Find the transformation matrix which represents the reflection on y-axis. 

5. What transformation does the matrix 

1001represent? Use this matrix to find the image of a point (2, 4).

6. Find a 2 × 1 matrix which transforms a point (a, b) into the point (a + 4, b – 5).Using the same 2 × 1 matrix transform the point (-4, 6). 

7. What transformation does the matrix 

0-1-10denote? Using the given matrix, find the image of the point A(5, -7).

8. Find a 2 × 1 matrix which transforms a point (a, b) into the point (a + 2, b – 3). Using the same 2 × 1 matrix transform the point (5, 7). 

9. If P(a, b) is transformed by 

0-2-20 to P'(-10, -8), find the value of a and b. 

10. Find 2 × 2 transformation matrix which transform the unit square into a parallelogram 

04620132. 

11. Find  2 × 2  matrix, which transforms   

02320351   into   03510232.

12. Find the 2 × 2 matrix which the unit square 

01100011 transform to a parallelogram 03410132..

13. A square ABCD with vertices A(2, 0), B(5, 1), C(4, 4) and D(1, 3) is mapped onto a parallelogram A'B'C'D' by a 2 × 2 matrix so that the vertices of the parallelogram are A'(2, 2), B'(7, 3), C'(12, -4) and D'(7, -5). Find the 2 × 2 transformation matrix. 

14. Find a 2 × 2  matrix, which transforms  a ∆PQR with vertices P(4, 3), Q(6, 4) and R(8, 1) into the ∆P'Q'R' with vertices P'(-3, -4), Q'(-4, -6) and R'(-1, -8 ). 

15. The square WXYZ has the vertices W(0, 3), X(1, 1), Y(3, 2) and Z(2, 4). Transform the given square WXYZ under the matrix 

  0  -1-1    0 and find the coordinates of the vertices of its image. 

16. ∆ABC having the vertices A(3, 6), B(5, -3) and C(-4, 2) is transformed by a 2 ×  2 matrix so that the co-ordinates of the vertices of its image are A'(-3, -6), B'(-5, 3) and C'(4, -2). Find the 2 ×  2 matrix. 

17. A square PQRS with vertices P(-2, 0), Q(-5, 1), R(-4, 4) and S(-1, 3) is mapped onto a parallelogram P'Q'R'S' by a 2 × 2 matrix so that the vertices of the parallelogram are P'(-2, -2), Q'(-3, -7), R'(4, -12) and  S'(5, -7). Find the 2 × 2 transformation matrix.