(Coordinate geometry is used to locate the position of a point on a plane with the
help of a pair of coordinate axes)
1. Coordinate Axes: Let
and
be two perpendicular lines
intersecting at O. The point O is called the origin and
(x-axis)
and
(y-axis) are called coordinate axes.
2. The distance of a point from the x-axis is called its y-coordinate, or
ordinate.
3. The distance of a point from the y-axis is called its x-coordinate, or
abscissa.
4. Distance formula:
a. Distance between two points [suppose, A(
plane
) and B(
)] on a
(
√(
)
(
)
)
(
)
Note: Since distance is always non-negative, we take only the positive value of the
square root.
b. Distance of a point A(
) from the origin O(
) on a plane.
√
5. Section formula:
a. The coordinates of the point A(
) which divides the line segment
) and Q(
)], internally, in the ratio
PQ [where, P(
are
(
)
Note: The coordinates of the point A(
) can also be derived by drawing
perpendiculars from P, A and Q on the y-axis and proceeding as above.
b. If the ratio in which A(
of the point A will be
) divides PQ is k : 1, then the coordinates
(
)
c. If the ratio in which A(
) divides PQ is 1 : 1, then the coordinates
of the mid- point A will be (Also known as the Mid-point formula)
(
)
(
)
6. Area of a triangle:
), Q(
a. The area of a triangle formed by the points P(
) is the numerical value of the expression
R(
[
(
)
(
)
(
) and
)]