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.
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.
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".
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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".
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C.
LOCUS FROM TWO FIXED POINTS
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.
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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.
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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.