**TOPIC 7: GEOMETRIC AND TRANSFORMATIONS ~ MATHEMATICS FORM 2**

**TOPIC 7: GEOMETRIC AND TRANSFORMATIONS ~ MATHEMATICS FORM 2**

**Reflection**

The Characteristics of Reflection in a Plane

Describe the characteristics of reflection in a plane

A transformation in a plane is a mapping which moves an object from one position to another within the plane.

Think of a book being taken from one comer of a table to another comer.

Figures on a plane of paper can also be shifted to a new position by a transformation.

The new postion after a transformation is called the image.

Examples of transformations are reflection, rotation, enlargement and translation.

**Different Reflections by Drawings**

The image in a mirror is as far behind the mirror as the object is in front of the mirror

PP’ is perpendicular to AB, RR’ is perpendicular to AB and QQ is perpendicular to AB.

The image of any point on the Q’ mirror line is the point itself.

PP’ is parallel to RR’ and QQ’

*y = x*

line y = x makes an angle 45° with the x and y axes. It is the line of

symmetry for the angle YOX formed by the two axes. By using the

isosceles triangle properties, reflection of the point (1, 0) in the

line y = x will be (0, 1).

reflection of (0,2) in the liney = x will be (2,0). You notice that the

co-ordinates are exchanging positions. Generally, the reflection of the

point (a,b) in the line y = x is (b,a).

Find the image of the point D(4,2) under a reflection in the x-axis.

Find the image of the point P(-2,5) under a reflection in the x-axis.

Point Q(-4,3) is reflected in the y-axis. Find the coordinates of its image.

Point R(6,-5) is reflected in the y-axis. Find the co-ordinates of its image.

Reflect the point (1 ,2) in the line y = -x.

Reflect the point (5,3) in the line y = x.

Find the image of the point (1 ,2) after a reflection in the line y=x followed by another reflection in the line y = -x.

Find

the image of the point P(-2,1) in the line y = -x followed by another

reflection in the line x = 0 ketch the positions of the image P and the

point P, indicating clearly the lines involved.

Find the co-ordinates of the image of the point A(5,2) under a reflection in the line y = 0.

Find the coordinates of the image of the point under a reflection in the line x = 0.

The co-ordinates of the image of a point R reflected in the x axis is R(2, -9). Find the coordinates of R.

on one object.

translation on the same point

**Solution**

**Reflection****Exercise 5**

transformation ABCD → A’B’C’D’ is a rotation around(-1, 2)by___°.Rotate

P around(-1, 2)by the same angle. (You may need to sketch things out on

paper.)P’ = (__,__)

transformation ABCD → A’B’C’D’ is a rotation around(-1, -3)by__°Rotate P

around(-1, -3)by the same angle. (You may need to sketch things out on

paper.)P’ = (__,__)