Geometrical Transformation Revision Questions Form Two Basic Mathematics
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 position after a transformation is called the image. Examples of transformations are reflection, rotation, enlargement and translation.
Different Reflections by Drawings
Represent different reflections by drawings
A reflection is a transformation which reflects all points of a plane in a line called the mirror-line. 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.
Some characteristics observed under reflection are:
- 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
The 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).
The reflection of (0,2) in the line y = 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).
The reflection of the point B (c,d) in the line y = -x is B’ (-d, -c)
Exercise 1
- 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.