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LOCI IT LESSON 1 - 4 STANDARD TYPES OF LOCI
(SEC 4 ELEMENTARY MATHEMATICS)

Software: JavaSketchpad (JSP)
Thinking Skills: Induction and Deduction
At the end of the lesson, the students should be able to:
(1)    describe the locus of a point P that is
        (a)    at a certain distance from a fixed point O,
        (b)    at a certain distance from a fixed line l or AB,
        (c)    equidistant from 2 fixed points A and B,
        (d)    equidistant from 2 fixed lines l and m,
(2)    construct the above loci.

 

A.  LOCUS FROM ONE FIXED POINT

It takes a few seconds to initialise the JavaSketch below. But if the toolbar at the bottom reads, "Applet not found", click here to troubleshoot.
 
Sorry, this page requires a Java-compatible web browser.  The first JavaSketch (IT4EMLoci1Point.gsp) shows a fixed point O and a variable point P. If the distance of P from O is always 2 cm, where can P move? 

Drag the point P and see the various positions that P can move to. Alternatively, click on the button "Animate"
 
Question 1: Infer by induction the locus of a point P that is always 2 cm from a fixed point O. 


Click here for answer (it shows animation in a different way).

 

B.  LOCUS FROM ONE FIXED LINE
 
Sorry, this page requires a Java-compatible web browser.  The second JavaSketch (IT4EMLoci1Line.gsp) shows a fixed (black) line AB and a variable point P (in 2 positions). If the distance of P from AB is always 1 cm, where can P move? 

Drag the point P and see the various positions that P can move to. Alternatively, click on the buttons "Animate" and "Animate". 
 
Question 2: Infer by induction the locus of a point P that is always 1 cm from a fixed line l


Click here for answer (it shows animation in a different way).

 

C.  LOCUS FROM TWO FIXED POINTS
 
Sorry, this page requires a Java-compatible web browser.  The third JavaSketch (IT4EMLoci2Points.gsp) shows 2 fixed points A and B and a variable point P (in 2 positions). If P is always equidistant from A and B, where can P move? 

Drag the point P and see the various positions that P can move to. Alternatively, click on the button "Animate". Don't be confused by the blue lines AP and BP. 
 
Question 3: Infer by induction the locus of a point P that is always equidistant from 2 fixed points A and B. 


Click here for answer (it shows animation in a different way).

 

D.  LOCUS FROM TWO FIXED LINES
 
Sorry, this page requires a Java-compatible web browser.  The fourth JavaSketch (IT4EMLoci2Lines.gsp) shows 2 fixed (black) lines l and m and a variable point P. If P is always equidistant from lines l and m, where can P move? 

Drag the point P and see the various positions that P can move to. Alternatively, click on the buttons "Animate" and "Animate". Don't be confused by the blue and pink lines. 
 
Question 4: Infer by induction the locus of a point P that is always equidistant from 2 fixed lines l and m


Click here for answer (it shows animation in a different way).

 

E.  EXERCISE

Apply what you have learnt to deduce the answers to this exercise. Please refer to the Maths Online IT Workbook for the exercise.
 

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