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Topic 7: Geometric And Transformations - Mathematics Study Notes Form II
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
Characteristics of Reflection
In the diagram, APQR is mapped onto ΔP’Q’R’ under a reflection in the line AB. If the paper is folded along the line AB, ΔPQR will fall in exactly onto ΔPQR.
The line AB is the mirror-line. which is the perpendicular bisector of PP’, QQ’ and ΔPQR and ΔP’Q’R are congruent.
- 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’
Reflection in the Line y = x
Exercise 1
1. Find the image of the point D(4,2) under a reflection in the x-axis.
2. Find the image of the point P(-2,5) under a reflection in the x-axis.
3. Point Q(-4,3) is reflected in the y-axis. Find the coordinates of its image.
4. Point R(6,-5) is reflected in the y-axis. Find the co-ordinates of its image.
5. Reflect the point (1 ,2) in the line y = -x.
6. Reflect the point (5,3) in the line y = x.
7. 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.
9. Find the co-ordinates of the image of the point A(5,2) under a reflection in the line y = 0.
10. Find the coordinates of the image of the point under a reflection in the line x = 0.
11. The co-ordinates of the image of a point R reflected in the x axis is R(2, -9). Find the coordinates of R.
Example 3
What type of transform takes ABCD to A’B’C’D’?
Solution
Exercise 5
What type of transform takes ABCD to A’B’C’D’?