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Name:………………………….
Grade: BE8 Section: A, B
Teacher: Zeinab Zeineddine
Abed Al – Karim Al – Khalil Public School
Test :Mathematics
Date: 8/5/ 2014.
Duration: 50 min
Translation and Vectors
I) 1) Vector: A vector MN

is characterized by a direction, a sense and a length.
Example the vector MN

has for direction (MN), for sense from M toward N, and for
length MN. (Length is also called module or magnitude).
2) Equality of vectors: Two vectors AB and CD
 
are equal if they have:
The same direction: (AB) and (CD) are parallel or coinciding or confounded.
The same sense: the sense from A to B is the same as that from C to D.
The same module: AB = CD.
B AB CD
 
Example A
C D means ABDC is a parallelogram
MI NK
 
MI KN
 
3) Two vectors AB and CD
 
are collinear if they held by the same straight line.
4) Two vectors AB and BC
 
are consecutive if the extremity of the first is the origin
of the second.
5) Two vectors AB and AC
 
have the same origin A.
6) Two vectors AB and CD
 
are opposite if they have same direction, same length,
and opposite sense. AB CD DC
  

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II) Translation is an operation that consists of displacing a geometric figure by sliding
it along a given straight line, a given distance, and a given sense.
We call translation of vector AB

the translation that goes from A to B.
Exercise 1: Mark M the image of M by the translation of vectorAB

.
Exercise 2: Draw (D ) the image of (EF) by the translation of vector AB

Exercise 3: Draw triangle A B C the image of triangle ABC by the translation of
vector BA

.

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Exercise 4: Draw (C )the image of C(O ; R) by the translation of vector BA

III) Sum of two consecutive vectors
1) Draw F the image of E by the translation of vectorAB

.
2) Draw I the image of F by the translation of vectorBC

.
3) The image point of E by the translation of vector AB

+ BC

is …………..
4) Draw the resultant vector of AB

+ BC

5) AB

+ BC

= ………… = …………..

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IV) Sum of any two vectors.
1) Draw F the image of E by the translation of vectoru

.
2) Draw I the image of F by the translation of vectorv

.
3) The image point of E by the translation of vector u

+ v

is …………..
4) Draw the resultant vector of u

+ v

5) u

+ v

= …………
V) Sum of two vectors having the same origin A.
1) Draw F the image of E by the translation of vectorAB

.
2) Draw I the image of F by the translation of vectorAC

.
3) The image point of E by the translation of vector AB

+ AC

is …………..
4) Draw the resultant vector of AB

+ AC

5) AB

+ AC

= ………… = …………..

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VI) Draw the resultant vector the sum of the two given vectors in each of the following
figures:
Mark E such that EE

AB

+ BC

Mark E such that EE

AB

+ AC
