FOR GMS ICSE 2014 23rd Aug

Dear Students, today we commence study of Ch 9 : REFLECTION

For the study of this chapter, you would need to use graph paper.
Kindly remember that drawing graphs is a work of art and neatness is the key.

• pencils should be sharpened well before drawing.
• do NOT use a rubber
• follow the following conventions :
• the X-axis and Y-axis are continuous lines and should be drawn with arrow heads at the ends of the lines.
• all writing on the graph must be IN PENCIL ONLY - do not use a pan at all.
• marking of numbers on the graphs should be below the X-axis and to the left of Y-axis
• look at the sum you are about to do and then decide by looking at the greatest value of the abscissa  and the greatest value of the ordinates and then decide on the length of the axis and the scale to be used. Generally use no less than 1cm = 1 unit.

 You have most probably studied 'Reflection' in Physics. However, our general understanding of reflection tells us that when an image is reflected it will be at the same distance behind the mirror / water as the object is in front of it.

In our study we will work at reflection in the X-axis (the line y = 0 - because the value of the ordinate on all points on this line will be 0); Y-axis (the line x = 0 - because the value of the abscissa on all points on this line will be 0) and through the Origin O (0,0) - the point of intersection of the X-axis and Y-axis.

Please look at pgs.117 / 118 : 9.5, 9.6 and 9.7 and the diagrams will show you what happens when a point is reflected in the X-axis, Y-axis and the Origin, respectively.

Note that if a point A is reflected, its reflection will be denoted as A'

Please note that a point remains unchanged under reflection in the following cases :

• when a point is reflected in the axis on which it lies
• when the origin (0,0) is reflected in the Origin, the X-axis and in the Y-axis

Now let's go to Ex 9 (A). Let's do sum nos 3, 4, 5, 6, and 7 first. Let us also do them graphically (i.e.draw the points and their reflection on a graph).

How will you do these sums ?

1. look at the points you have to reflect - name them A, B and C.
2. check the value of the abscissa and ordinates and see what length you will need to draw the X-axis and Y-axis e.g. in No.3 the values of the  abscissa are from -5 to + 3 - so you will draw the X-axis from -6 to +4. Since the values of the ordinates are from 0 to 4, you will draw the Y-axis from +5 to -5. Why to -5 in the Y-axis? because since the points are reflected in the X-axis the values of the ordinates in the reflect points will be the opposite of the ordinates in the original points.
3. plot point A. plot its reflection - what will its ordinates be ? The coordinates of the reflected point will be (3, -2)
4. Now do the same with the other sums
5. Check you answers (after you have tried, please !)

All the best !