Page 274 - MATHEMATICS COURSE FOR SECONDARY SCHOOLS BOOK 2

(b) (i) O (0, 0) is the start point and P (-9, -5) is the end point of OP. determine OP in the form ( xy )
(ii) Evaluate the size of OP. The position
DISPLACEMENT
vector, OP =
y
-9
0
-5
P -5
x
Given two points, the start point and the end point or a vector can always find the displacement vector in the form( xy )
EXAMPLE 5
(a) A(2,1) is the start point and B((7,4) is the end point of AB. Find the displacement vector AB, in the form ( xy )
(b) P(2,5) and Q(10,2) are the start point and end point of PQ.
Calculate the displacement vector PQ, as a column vector.
(c) MN is formed by the points M(9,6) and N(3, 2). Determine the displacement MN, in the form ( xy )
(d) The points x(2, 7) and y(9, 2) defines XY. Evaluate the displacement vector, XY.
(a) Plot the points A(2, 1 )and B(7, 4) on graph paper, then complete a right-angled triangle indicating the movement from A to B.
VECTOR GIVEN TWO POINTS
The size of OP, OP =√(-92 + (-5)2 = √81+25 = √106 = 10.3 units (correct to 3 s.f.)
( xy ) State the position vector
A point P(x, y) has a position vector
EXERCISE 13.3
1. (a)
(b) Find the magnitude of OA.
represented by the point A(7, 4).
2. (a)
(b) Calculate the size of OP.
State the position vector represented by the point P( -5, 8).
3. (a)
(c) Find the magnitude of OK
State the position vector represented by the point K(9, -6).
4. (a)
(b) Calculate the size OX.
State the position vector represented by the point X(-8, -10).
268
-9 OP =(-5 )
OP = 10.3 units