1. Applications in Coordinate Geometry
Section 8.8
Applications in Coordinate Geometry

2. Representation
P(x, y)
Each point P(x, y) on the coordinate plane can be represented by the 21 matrix

3. Matrix representation of the transformation
Q(x’, y’)
P(x, y)
Suppose each point P(x, y) on the coordinate plane is to be transformed to its mirror image Q(x’, y’) about the y-axis.
Matrix representation of the transformation

4. Reflection about the x-axis
P(x, y)
Q(x’, y’)
Matrix representation of the transformation

5. Reflection about the line y = x
Q(x’, y’)
P(x, y)
Matrix representation of the transformation

6. Reflection about y = (tan)x
Q(r, 2 - a)
Matrix representation of the transformation
P(r, a) r

7. 1998 Paper I Q.2 (P.279 Q.20)
(x, y)  (-x, y):
(x, y)  (y, x):

8. 1999 Paper I Q.6 (P.279 Q.21)
y = (tan a)x 
y = ½ x  ? 1 2

9. 1999 Paper I Q.6(b)

10. 1999 Paper I Q.6(c) By (b), (x2, y2) = (8, -1) + (0, 3) = (8, 2).
(4, 7)
(4, 10)
By (b), (x2, y2)
= (8, -1) + (0, 3)
= (8, 2).
x2 = 8, y2 = 2
(8, 2)
(8, -1)

11. Rotation through an angle 
Q(r, a + )
Matrix representation of the transformation
P(r, a) r

12. What should be its inverse?
If M is its inverse, then
Rotation through 
Rotation through -

13. Don’t Confuse Them! Rotation through an angle  determinant = 1
Reflection about the line y = (tan )x
determinant = -1