Additional Mathematics
Chapter 5 Co-ordinate Geometry – The Straight Line
ANSWERS FOR ENRICHMENT ACTIVITIES
Just for Fun (pg 114)
The third man will either see two white hats or one black and one white hat because if he
sees two black hats, he would have known that he is wearing a white hat. The second
man must have seen a white hat because if he sees a black hat, he would have known that
he must be wearing a white hat from the third man’s response. Thus the first man knows
that he can only be wearing a white hat from the other two men’s response.
Just for Fun (pg 107)
The lengths of SR and PQ are equal in all the three cases. We may feel that
PQ  RS in (a)
PQ  RS in (b)
and
PQ  RS in (c)
Try measuring the lengths of PQ and RS with a ruler.
This is due to optical illusion.
Teachers’ Resource NSAM
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Geometer’s SketchPad(GSP) WS-5-1Coordinate Geometry
1. We can use the GSP to show by inference that the product of the gradients of two
perpendicular lines is equal to -1.
2. At
choose Display and Preferences and Autoshow for Points and Straight
objects. Select the Precision for the slope measure and Distance as tenths.
3. At
select Graph, Show Axes and Show Grid.
4. At
choose Graph and then Plot points. A panel will appear where you can enter
the co-ordinates of the points you want to plot. Plot three points and choose
Free Points so that we can move the points later on.
5. Join the points CD and CE with
.
6. Use
to select the line j and from the Measure menu, choose Slope to measure
the
slope or the gradient of the line j. Find the gradient of the line k in the
similar manner.
7. Select Measure and Calculate to find the product of the gradients j and k by clicking
slope j from the screen and * the slope k from the screen. Then click OK.
8. Use
of
to move the points C, then D and then E to see how the values of the slopes
the lines are measured and the products are calculated for you.
9. Use
to select the point D and with shift key on, select points C and E and
choose Angle from the Measure Menu to measure the angle DCE.
Teachers’ Resource NSAM
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10. Drag the point D until the angle DCE is 90 degrees. What do you notice about the
product of the gradients of the two lines, j and k?
11. Conclusion: _________________________________________________________
Teachers’ Resource NSAM
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