Coordinate geometry

2. SOME BASIC POINTSSOME BASIC POINTS
To locate the position of a point on aTo locate the position of a point on a
plane,we require a pair of coordinate axes.plane,we require a pair of coordinate axes.
The distance of a point from the y-axis isThe distance of a point from the y-axis is
called itscalled its x-coordinatex-coordinate,OR,OR ABSCISSA.ABSCISSA.
The distance of a point from the x-axis isThe distance of a point from the x-axis is
called itscalled its y-coordinatey-coordinate,OR,OR OrdINATE.OrdINATE.

3. X
Y
Y
/
X
/ 0
P(x , y )
y
x

4. Distance formulaDistance formula
To find the distance between any twoTo find the distance between any two
points P(xpoints P(x11 ,y,y11) and Q(x) and Q(x22 ,y,y22).).
P
Q ( x2 , y2)
(x1,y1)
X
Y
0
R S
T
X 2-X1
Y2 – Y1
X
/
Y
/

5. Then, OR = xThen, OR = x11 , OS = x, OS = x22
So , RS = xSo , RS = x22 – x– x11 = PT= PT
• Also , SQ = yAlso , SQ = y22 , ST = PR = y, ST = PR = y11
So , QT = ySo , QT = y22 – y– y11
 Now applying the Pythagoras theorem inNow applying the Pythagoras theorem in ∆PTQ , we get∆PTQ , we get
PQPQ22
= PT= PT22
+ QT+ QT22
= ( x= ( x22 – x– x11 ))22
+ ( y+ ( y22 – y– y11))22
ThereforeTherefore
PQ = √(xPQ = √(x22 – x– x11))22
+ ( y+ ( y22 – y– y11))22
So the distance between points P(xSo the distance between points P(x11 ,y,y11),Q(x),Q(x22,y,y22))
isis √(x√(x22 – x– x11))22
+ ( y+ ( y22 – y– y11))22
,which is called the,which is called the DISTANCEDISTANCE
FORMULA.FORMULA.

6. QuestionsQuestions
Find the distance between the followingFind the distance between the following
pairs of points:pairs of points:
i) ( 2,3) , (4,1) (ii) (-5,7) , (-1,3)i) ( 2,3) , (4,1) (ii) (-5,7) , (-1,3)
Check whether (5,-2),(6,4) and (7,-2) areCheck whether (5,-2),(6,4) and (7,-2) are
the vertices of an isosceles triangle.the vertices of an isosceles triangle.
Find the point on the x-axis which isFind the point on the x-axis which is
equidistant from (2,-5) and (-2,9).equidistant from (2,-5) and (-2,9).
Prove that the diagonals of a rectangleProve that the diagonals of a rectangle
bisect each other and are equal.bisect each other and are equal.

7. x/
P
Q(x2, y2 )
R(x, y)
m
n
( x1,y1)
O X
Y
Y/
S
T
x-x1
x2-x
y-y1
Y2 - y

8. Questions:Questions:
• Determine the ratio in which the line 3x + yDetermine the ratio in which the line 3x + y
– 9 = 0 divides the segment joining the– 9 = 0 divides the segment joining the
points (1,3) and (2,7)points (1,3) and (2,7)
• Find the ratio in which the point (-3, p)Find the ratio in which the point (-3, p)
divides the line segment joining the pointsdivides the line segment joining the points
(-5,-4) and (-2,3). Hence, find the value of(-5,-4) and (-2,3). Hence, find the value of
p.p.

9. A(x1, y1)
C(x3 , y3 )
B(x2, y2)
Y
Y/
X/
XO
x1 – x2 x3 - x1
y1
y3
y2
D E F

10. THANK YOU