Maths : Coordinate Geometry: Points to remember

**Points to remember**

**• **If *x _{1}, x_{2}*
are the

**• **If *y _{1}, y_{2}*
are the

**• **Distance between the two points ( *x _{1},
y_{1}* ) and (

**• **Distance between ( *x _{1},
y*

**• **The mid-point M of the line segment joining
the points A(*x*_{1}, *y*_{1}) and B(*x*_{2}, *y*_{2} ) is

**• **The point P which divides the line segment
joining the two points A(*x*_{1},
*y*_{1}) and B(*x*_{2}
, *y*_{2} ) internally in the ratio
*m:n* is

**• **The centroid G of the triangle whose
vertices are *A* (*x*_{1} , *y*_{1} ), *B* (*x*_{2}
, *y*_{2} ) and *C* (*x*_{3} , *y*_{3}
) is

**• **The centroid of the triangle obtained
by joining the mid-points of the sides of a triangle is the same as the centroid
of the original triangle.

**Activity**

Plot the points *A*( 1, 0), *B* ( –7, 2), *C* (–3,
7) on a graph sheet and join them to form a triangle.

Plot the point *G* ( –3, 3).

Join *AG* and extend it to intersect *BC* at *D*.

Join *BG* and extend it to intersect *AC* at *E*.

What do you infer when you measure the distance between *BD*
and *DC* and the distance between *CE* and *EA*?

Using distance formula find the lengths of *CG* and *GF*,
where *F* in on *AB*.

Write your inference about *AG: GD, BG: GE* and *CG: GF*.

**Note**:

** G **is the

Tags : Coordinate Geometry | Maths , 9th Maths : UNIT 5 : Coordinate Geometry

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9th Maths : UNIT 5 : Coordinate Geometry : Points to remember | Coordinate Geometry | Maths

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