1. The document discusses vectors and their properties including direction, sense, length, equality of vectors, collinear vectors, consecutive vectors, opposite vectors, and translation. 2. Translation is defined as displacing a geometric figure along a given straight line a given distance and direction. The translation of a vector AB moves from point A to B. 3. Sections discuss summing consecutive vectors, any two vectors, and vectors with the same origin by translating points using the vectors. Exercises involve drawing images of figures under translations and finding resultant vectors.

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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

= ………… = …………..

4. 4/5
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
