Unit 4 - Activity 3

ACTIVITY 4.3
DIVISION OF A SEGMENT IN MORE THAN TWO PARTS

Imagine now that we want to divide a segment AB in three equal parts, that is to say, to find two points P₁ and P₂ of the segment that it divides its in three equal parts.

These points P₁ and P₂ verify:

Since then, we can get P₁ and P₂ making a translation of the point A according to vectors
₁ and ₂ respectively:

With A(a₁,a₂) and B(b₁,b₂), these last results tell us that the points P₁ and P₂ are:

INTERACTIVE ACTIVITY

Find the coordinates of two points P₁and P₂ that divides the segment AB in three equal parts in next cases.

Check the results using the applet of the right later.

a) A(5,3) and B(-4,-3)

b) A(0,-4) and B(-3,5)

c) A(-5,1) and B(1,6)

d) A(2,-2) and B(-3,2)

SOLUTION

HOMEWORK

(Do you want a Word document prepared for making this work ?)

Being A(a₁,a₂) and B(b₁,b₂), and now you suppose that you want to divide segment AB in five equal parts by the points P₁, P₂, P₃ and P₄. Show that these four points can get from the formulas:

END OF ACTIVITY 4.3
DIVISION OF A SEGMENT IN MORE THAN TWO PARTS

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