COORDINATE GEOMETRY
relationship between algebra and geometry.
In Class IX, you have studied that to locate the position of
a point in a plane, we require a pair of coordinate axes.
What is Coordinate Geometry ?
The number associated on the foot of
the perpendicular on X-axis is called
X-coordinate or abscissa.
The number associated on the foot of
the perpendicular on Y-axis is called
Y-coordinate or ordinate.
The horizontal axis is called x-axis
and the vertical axis is called y-axis.
The intersection point of both the axes
is called the origin
and they intersect at right angle.
X
Y
O
origin
P
x
(x, y)
Consider point P
Let us draw perpendicular to Y-axis
Let us draw perpendicular to X-axis
Now, let us understand
its X-coordinate and
Y-coordinate
y
Let us learn how to find the
distance between the two points
whose coordinates are given,
The coordinates of a point on the
X-axis are of the form (x, 0),
and of a point on the Y-axis are
of the form (0, y).
X
Y
O
P
(__,__)
Q
We know that,
Y-coordinate of any point on X-axis is ‘0’
We know that,
X-coordinate of any point on Y-axis is ‘0’
x
0
(__,__)
y
0
Consider a point on X-axis
Consider a point on
Y-axis
Let us find their coordinates
X
O
Y
DISTANCE FORMULA
Distance formula is used to find the distance between
two points in a co-ordinate plane.
A
B
AB =
The distance between two points A(x1, y1) and
B(x2, y2) in a rectangular coordinate system
is given by
(x2 , y2)
+
–
–
(
)
(
)
(x1 , y1)
x2
x1
y2
y1
2
2
Let coordinates of point A be (x1, y1)
Let coordinates of point B be (x2, y2)
Q. Find the distance between the following pair of points :
(i) A (2, 3) , B (4, 1)
Sol.
∴ AB =
+
–
–
(
)
(
)
x2
x1
y2
y1
2
2
+
–
–
(
)
(
)
4
2
1
3
2
2
+
(
)
2
2
(
)
–2
2
+
4
4
8
2
2
units
What is the formula to find distance between two points ?
x1 = 2,
y1 = 3,
x2 = 4,
y2 = 1
Let the coordinates of B be (x2, y2).
Let the coordinates of A be (x1, y1).
By distance formula,
Let us substitute the values.
AB =
∴ AB =
∴ AB =
∴ AB =
∴ AB =
+
–
–
(
)
(
)
x2
x1
y2
y1
2
2