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COORDINATE GEOMETRY - CLASS X
● Two perpendicular lines intersecting
at origin are called Coordinate
axes
...

● A point P in the cartesian plane is
represented as P(x,y) where x = x
coordinate and y = y coordinate
● The coordinates of a point on the
X axis= (x,0)
Y axis= (0,y)

Section Formula:
● The coordinates of a point R(x,y)
which divides the line segment
P(x1,y1) and Q(x2,y2) internally in the
ratio m:n is:

R

where x =

and y =

● The coordinates of a point R(x,y)
which divides the line segment
P(x1,y1) and Q(x2,y2) externally in
the ratio m:n is :

R

where x =

y=

● Special case: Mid point Formula
The mid-point of a line segment that
divides the line segment in the ratio
1: 1 is

Area of a Triangle

● 𝐴𝑟𝑒𝑎 = 1/2( 𝑏𝑎𝑠𝑒 𝑥 𝑎𝑙𝑡𝑖𝑡𝑢𝑑𝑒)

● Three points A, B and C are the
vertices of an equilateral triangle if
AB = BC = CA
● The points A, B and C are the
vertices of an isosceles triangle if
AB = BC or BC = CA or CA = AB
● Three points A, B and C are the
vertices of a right triangle, if
AB 2 + BC 2 = CA 2
Notes:
● Three points A, B and C are collinear
if the distances AB, BC and CA are
such that the sum of two distances
is equal to the third
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●

If AB = BC = CD = DA; AC ≠ BD, then
ABCD is a rhombus
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● If ABCD, BC = DA; AC ≠ BD, then
ABCD is a parallelogram
...

● Diagonals of rhombus and square
bisect each other at right angle
...
In
the figure, G is the centroid of a
triangle ABC
...

● If x ≠ y, then (x, y) (y, x) and if (x, y) =
(y, x), then x = y

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