## Coordinate Geometry

## Coordinate Axis

## Distance Between Two Points (x_{1}, y_{1}) and (x_{2}, y_{2})

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 (x_{1}, y_{1}) and (x_{2}, y_{2}) **Internally** in ratio **m:n**

**Internally**

**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 (x_{1}, y_{1}) and (x_{2}, y_{2}) **Externally** in ratio *m:n*

**Externally**

### 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 (x_{1}, y_{1}) and B (x_{2}, y_{2})

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 (x_{1}, y_{1}) , B (x_{2}, y_{2}) & C (x_{3}, y_{3})

### 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 (x_{1}, y_{1}) , B (x_{2}, y_{2}) & C (x_{3}, y_{3})

### 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)