Coordinate Geometry

Coordinate Geometry

 

Coordinate Axis

Distance Between Two Points (x1, y1) and (x2, y2)

Distance between two points (x1,y1) and (x2,y2) is:

Example:

What is the distance between two points (-1,2) & (7,8)

 

If a point P(x, y) divides the line joining (x1, y1) and (x2, y2) Internally in ratio m:n

Example:

Find the coordinates of the point which divides the line joining the points (2, 3), (5, 6) internally in the ratio 2:1

 

If a point P(x, y) divides the line joining (x1, y1) and (x2, y2) Externally in ratio m:n

Example:

A (4, 5) and B (7, - 1) are two given points and the point C divides the line-segment AB externally in the ratio 4 : 3. Find the co-ordinates of C.

 

Cooordinate of line Joining the mid points of A (x1, y1) and B (x2, y2)

The coordinates of the midpoints is:

Example:

What are the mid points of the line joining two points (3,4) & (5,-2) is:

 

Area of a triangle whose vertices are A (x1, y1) , B (x2, y2) & C (x3, y3)

Example:

The area of the triangle whose vertices are A(3,8), B(-4,2) and (5,-1)(in sq units) is:
a) 37.5
b) 28.5
c) 75
d) 57
 

Condition of Collinearity

If three points are collinear, then the area of triangle should be zero.

Example:

Show that the points (0, -2) , (2, 4) and (-1, -5) are collinear. 

 

Centroid of a triangle whose vertices are A (x1, y1) , B (x2, y2) & C (x3, y3)

Example:

The coordinates of the centroid of Triangle ABC with vertices A(-1,0), B(5,-2) and C(8,2) is:
a) (6,0)
b) (0,6)
c) (12,0)
d) (4,0)