Coordinate Geometry
* 1. Introduction :
3. Coordinates of a Point :
In Coordinate Geometry
Any point P on the plane is
we
Study geometry using points represented by an ordered pair (x,y)
and numbers (coovdinates). where x is the x- coordinate and
4 is the y coordinate.
2. Cartesian Plane :
A plane formed by two
pexpendicular number lines 4 ,P(z.y)
called X-axis and 4 - axis
I
(-, +) (+, +)
4. Distance Formula :
(-,-) (+,-) If P(,, y.) and Q (x, ya) are
two points, then the distance
between them is
5 Section Formula : PQ =
If P(,, y,) and Q(4, y.) divide the
line segment in the ratio m: m
6. Midpoint Formula :
internally at R, then
m y2 + nyi If P(x, 9.) and Q(x y) are
R( m + m m + n
two points, then the midpoint M
If the division is external, then of PQ is
R mx, - nx, m y2 - ny. M * X,
m- n m - m 2 2
7. Area of Triangle :
If the vertices of a triangle are A (x, 9.), B (*4, ya) and C (13,9),
then the area
Practice more
to get better
Area = |x,(y-y) + x(-9)+ X, (y-9)|
* 1. Introduction :
3. Coordinates of a Point :
In Coordinate Geometry
Any point P on the plane is
we
Study geometry using points represented by an ordered pair (x,y)
and numbers (coovdinates). where x is the x- coordinate and
4 is the y coordinate.
2. Cartesian Plane :
A plane formed by two
pexpendicular number lines 4 ,P(z.y)
called X-axis and 4 - axis
I
(-, +) (+, +)
4. Distance Formula :
(-,-) (+,-) If P(,, y.) and Q (x, ya) are
two points, then the distance
between them is
5 Section Formula : PQ =
If P(,, y,) and Q(4, y.) divide the
line segment in the ratio m: m
6. Midpoint Formula :
internally at R, then
m y2 + nyi If P(x, 9.) and Q(x y) are
R( m + m m + n
two points, then the midpoint M
If the division is external, then of PQ is
R mx, - nx, m y2 - ny. M * X,
m- n m - m 2 2
7. Area of Triangle :
If the vertices of a triangle are A (x, 9.), B (*4, ya) and C (13,9),
then the area
Practice more
to get better
Area = |x,(y-y) + x(-9)+ X, (y-9)|
