BEHAVIOUR OF GRADIENT BETWEEN TWO POINT
-Lets two points be 
which can be used to form the line AB.
(i) If 
, and 
the line increase from left to right imply positive slope.
(ii) If 
the line decrease from right to left imply 
slope.
(iii) If 
the line is horizontally with zero gradient
(iv) If 
the line is vertical with infinity gradient
COLLINEAR POINTS
– – Are point which lie on the same straight line
Where,
A, B, and C are collinear.
– – The condition of collinear points have the same slope/ gradient
Note:
If A (
); B 
and C 
are collinear then the area of 
= 0.
Example 1
1. 1.Determine the value of K such that following points are collinear:-
a) 
and 
b) 
and 
2. Show that the points 
, and 
are collinear.
3. The straight line 
Cut the curve 
at P and Q. Calculate the length PQ.
4. If A and B are products of OX and OY respectively. Show that xy=16. If the area of 
is 8 units square.
Solution:
A 
B
, C 
For collinear point
2. Give
; B 
C 
Alternatively
Since the area of ΔABC is 0 unit hence the points are collinear.
3. Given
4. Given
Since
Area of ΔOAB = 8 square units
Then,
5. If 
and 
are the collinear of midpoint of the line forming the points 
and 
show that, x-y+1=0.
Solution
M.P = (x, y)
A 
and B 
Required 
