Transformation

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EXERCISE … TRANSFORMATION WITH MATRICES
1) a) Draw x- and y – axis with values from – 8 to +8.
b) Draw the triangle A(2, 2), B(6, 2) and C(6, 4). Find the image under the transformation
represented by the following matrices.

i)

 0  1
 
 1 0

(ii)

 1

0

0

1

(iii)

1

0

0

- 1

(iv)

0

1

  1

1

0

(v)

c) Describe a single transformation which maps:
(i) A1B1C1 onto A2B2C2
(ii) ABC onto A4B4C4

1
2

 
 1 1
 2

2) a) On a graph paper draw a triangle T whose vertices are (2, 2), (6, 2) and (6, 4).
b) Draw the axes from – 8 to +8 using a scale of 1cm to represent 1 unit on each axis.

c) Draw the image U of T under the transformation whose matrix is

d) Draw the image V of T under the transformation whose matrix is

0

1
1

0

e) Draw the image W of T under the transformation whose matrix is

f) Draw the image X of T under the transformation whose matrix is

1

0
0

-1

.

.

 0 -1
 
 1 0
 1 - 3
 
 0 1
.

.

g) Describe a single transformation which would map U onto V.

3) a) Draw L(1, 1), M(3, 3) and N(4, 1) and its image L’M’N’ under the matrix A =

b) Find and draw the image of L’M’N’ under the matrix B =

 0 1
 
 1 0

1

0

0

-1

and label it as L’’M’’N’’

c) Calculate the matrix product BA.
d) Find the image of LMN under the matrix BA, and compare with result of performing BA(LMN).
(Axes: Both axes from -5 to +5 using a scale of 1cm to 1 unit).

4) a) Draw P(0, 0), Q(2, 2) and R(4, 0) and its image P’Q’R’ under the matrix A =

b) Find and draw the image of P’Q’R’ under the matrix B =

c) Calculate the matrix product BA.

1

0

1

1

2

0

0

2

.

and label it as P’’Q’’R’’

d) Find the image of PQR under the matrix BA, and compare with result of performing BA(PQR).
(Axes: x –axis 0 to +6 and y axis 0 to +9)

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