J20

(i) Find the coordinates of A 4, B 4 and C 4.
(ii) Describe transformation S fully.
13. Triangle ABC has its vertices at A(6, 0), B(9, 2) and C(6, 2).
(a) Determine the coordinates of the vertices of its image, A1B1C1, after a
transformation P, where P represents a reflection in the line
y = 3.
(b) If Q represents an anticlockwise quarter-turn about the point (2, 3),
determine the coordinates of the vertices of triangle A2B2C2, the image of
triangle A1B1C1 under transformation Q.
14. The vertices of ∆PQR are P(1, 1), Q(2, 2) and R(0, 3).
(a) Draw and label ∆PQR.
(b) The vertices of ∆P1Q1R1 are found at P1(-2, 2), Q1(-3, 3) and
R1(-4, 1). Draw and label ∆P1Q1R1.
(c) Describe fully the single transformation that maps ∆PQR onto ∆P1Q1R1.
(d) Triangle PQR can also be mapped onto ∆P1Q1R1 by an anticlockwise rotation
of 90 0 about the origin, followed by a translation. Write down the column
vector which represents this translation.
15. (a) Draw the axes so that both x and y can take values from -2 to +8.
(b) Draw triangle ABC at A(2, 1), B(7, 1), C(2, 4).
(c) Find the image of ABC under the transformation represented by the matrix
1
1
and plot the image on the graph.
1
1
(d) The transformation is a rotation followed by an enlargement. Calculate the
angle of the rotation and the scale factor of the enlargement.
16. (a) On graph paper, draw the triangle T whose vertices are (2, 2), (6, 2) and (6,
4).
(b) Draw the image U of T under the transformation whose matrix is
0
1
.
1
0
(c) Draw the image V of T under the transformation whose matrix is
1
0
.
0
1
(e) Describe the single transformation which would map U onto V.
17. (a) Find the images of the points (1, 0), (2, 1), (3, -1), (-2, 3) under the
1
3
transformation with matrix .
2
6
(b) Show that the images lie on a straight line, and find its equation.
2
3
18. The transformation with matrix maps every point in the plane onto a line.
6
9
Find the equation of the line.