Unit 4 - Activity 1

ACTIVITY 4.1
MIDPOINT OF A SEGMENT

They give you two points A and B, the midpoint of the segment AB is the point M which divided its in two segments AM and MB of equal length.

We can get point M moving point A according to the vector , or vector B according to vector . Make translations is equivalent to sum vectors (see activity 2.7), we have:

M = A +
M = B +

We consider the first of the two previous equalities. If M is the midpoint of AB, it verifies .
In addition, we can get vector making the difference between B and A, that is = B – A.

Linking all previous equalities, we have:

If A(a₁,a₂) and B(b₁,b₂), this result says to us that the midpoint M of the segment AB is:

INTERACTIVE ACTIVITY

You calculate the midpoint M of the segment AB in the next cases.

Use firstly the formula and check after in the right applet that M it is got when .

1) A(2,6) and B(10,2)

2) A(-1,1) and B(9,5)

3) A(6,-2) and B(-1,5)

4) A(0,0) and B(3,7)

5) A(-4,2) and B(4,-2)

SOLUTION

HOMEWORK

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

You draw a triangle with vertexesA(1,-3 ), B(-3,5) and C(5,7), you calculate the coordinates of the midpoints of each of its sides and locate them in the corresponding places.

END OF ACTIVITY 4.1
MIDPOINT OF A SEGMENT

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