BBA I Business Maths Coordinate geometry

1.  Coordinate Geometry
 Course: BBA
 Subject: Business Mathematics
 Unit-4
1
2

2. Co-ordinate system in two dimension:
Suppose two straight lines XOX’ and YOY’
intersect each other at right angle at the point
o in the plane of paper.
The line XOX’ is called x-axis and line YOY’
is called y-axis.
The point o is called the origin.
Two lines also called co-ordinate axes.
They divide the plane in to four parts or
regions namely XOY, X’OY, X’OY’ and
XOY’.
These regions are respectively called first,
second, third and fourth quadrants.

3. 3

4. 4

5. 5

6. Distance between two points:
Let P and Q be feet of perpendiculars on the
X-axis of the points A and B and let R and S
be feet of perpendiculars on the Y-axis of
these points.
In right angled ΔABC,
AB2 = AC2 + BC2
= PQ2 + RS2
=
   
2 2
2 1 2 1AB x x y y   
   
2 2
2 1 2 1x x y y  

7. Slope of a line:
 Let A(x1, y1) and B(x2, y2) be any two
points where x1 ≠ x2 i.e. AB is not parallel
to Y-axis.
 Then the slope m of the line AB is defined
as
m =
=
y-coordinates
x-coordinates
difference of
difference of
1 2
1 2
y y
x x



8. Slope of parallel and perpendicular lines:
 Let l1 and l2 be two lines having slopes m1
and m2 respectively. Then
(1) If m1 = m2, then and then l1 ║ l2
(2) If m1 * m2 = -1, then and then l1┴ l2

9. (1) Equation of a line joining two points:
 Let A(x1, y1) and B(x2, y2) be two points in
the plane XOY, where x1 ≠ x2 and y1 ≠ y2.
 Let P(x, y) be any point on the line AB.
 Thus, the point A, P and B are collinear.
slope of = slope of AP AB
6

10. (2) Equation of line passing through
A (x1, y1) and having slope m:
 Let the slope of the line l be m.
 Let A (x1, y1) be a point on the line l.
 Let P (x, y) be any point on the line l.
 Now, slope of line AP = slope of l
 y – y1 = m (x – x1)
 This is the required equation of the line l.
1
1
y y
m
x x

 


11. (3) Equation of a line having slope m
and making intercept c on Y-axis:
 Suppose the line l has slope m and it makes an
intercept of length c on Y-axis.
 Hence A (0,c) is a point on the line l.
 Let P (x,y) be any point on the line l.
 Hence slope of line AP = slope of l.
 Therefore, y – c = mx
 Y = mx + c
 This is the required equation of the line l.
0
y c
m
x

 


12. (4) Equation of line making
intercepts a and b on the axes:
 Suppose a line l makes an intercept of
measure ‘a’ on X-axis and ‘b’ on Y-axis.
 Hence A (a,0) and B (0,b) are the points on
the axes.
 Let P (x,y) be any point on the line l.
 Now, slope of line AP = slope of line AB
0 0
0
y b
x a a
 
 
 

13. y b
x a a

 

Therefore, ay = - b (x –a)
ay = -bx + ab
ay + bx = ab
Dividing both sides by ab, we get
This is required equation of the line l.
1
x y
a b
 

14. (5) General equation of a line.
 The general form of the equation of a line
is Ax + By + C = .
 Now, find the slope and intercepts on axes
of this line.
 Ax + By + C = 0
Therefore, By = -Ax - C
Dividing both sides by B, we get
0.
A C
y x ifB
B B
   

15. Comparing this equation with y = mx + c,
we get
Also, Ax + By + C = 0 gives Ax + By = -C.
Comparing this with x/a + y/b = 1, we get
( )
( )
( )
A coefficientof x
slope m
B coefficientof y
   
1
Ax By
C C
  
 
1
x y
C C
A B
  
 

16. Intercept on X-axis
=
Intercept on Y-axis
=
tanC cons tterm
A coefficientofx

 
.C C T
B coefficientofy
  

17. References:
1.https://encryptedtbn0.gstatic.com/images?q=tbn:ANd9GcS31l2u1ZJXzT1hb2F
6pV_SRWiSrlSbuEXD1DvryIN8k7Wv2AOa
2.http://www.google.co.in/imgres?imgurl=http%3A%2F%2Fupload.wikimedia.o
rg%2Fwikipedia%2Fcommons%2Fthumb%2Fc%2Fcb%2FPunktkoordinaten.
svg%2F350px-
Punktkoordinaten.svg.png&imgrefurl=http%3A%2F%2Fen.wikipedia.org%2
Fwiki%2FAnalytic_geometry&h=292&w=350&tbnid=5YT3yeaKnQ9oyM%
3A&zoom=1&docid=H9yuqNHXa-
wKTM&ei=QZWjVITTEM6OuAS4zYHYCQ&tbm=isch&ved=0CDcQMygI
MAg&iact=rc&uact=3&dur=973&page=1&start=0&ndsp=12data:image/png;
base64,iVBORw0KGgoAAAANSUhEUgAAAPYAAADNCAMAAAC8cX2
UAAABIFBMVEX////w8PD39/f7+/vp6enk5OT09PQAAABwcHAAAP//=
3. http://0.tqn.com/y/math/1/S/o/E/cart1.gif
4.http://img.sparknotes.com/content/testprep/bookimgs/newsat/0003/coordinate.g
if
5.https://encryptedtbn0.gstatic.com/images?q=tbn:ANd9GcRaf7mQU-
NMqV23jKjJou2KKVvJ3y8A__EYz7rQEOUUIVSaosdgPg
6.https://encryptedtbn0.gstatic.com/images?q=tbn:ANd9GcRX_X4grNbThKorT
RuH6YfQBYZo5eOS4LYhaoUw3BufKO0flS9N
7. Business Mathematics by G. C. Patel and A.G. Patel – Atul Prakashan
(content)