Coordinate Geom...

$$ \mathrm{ABC} $$ is a triangle and $$ \mathrm{D} $$ is a mid point of $$ \mathrm{BC} $$. If the co-ordinate of vertices of $$ \triangle \mathrm{ABC} $$ are (1,2),(-1,-3) and (3,-5) respectively then co-ordinate of the point divides $$ A D $$ internally in the ratio 2: 1 will be :

The coordinated of the midpoint of the line segment joining points (6,8) and (2,4) will be:

The line $$\displaystyle 3x+2y=24$$ meets x-axis at A and y-axis at B. The perpendicular bisector of $$\displaystyle \overline { AB } $$ meets the line through (0, -1) and parallel to x-axis at C. Find the area of $$\displaystyle \Delta ABC$$.

If the coordinates of the mid points of the sides of a triangle are $$(1,2),(0,-1)$$ and $$(2,-1)$$. Find the coordinates of its vertices.

If four points are $$A(6,3),B(-3,5),C(4,-2)$$ and $$P(x,y),$$ then the ratio of the areas of $$\triangle PBC$$ and $$\triangle ABC$$ is:

$$\text{Q}, \text{R}$$ and $$\text{S}$$ are the points on the line joining the points $$\text{P}(a, x)$$ and $$\text{T}(b, y)$$ such that $$\text{PQ=QR=RS=ST}$$, then $$\displaystyle \left ( \frac{5a+3b}{8}, \frac{5x+3y}{8} \right )$$ is the mid point of the segment :

The lengths of the medians of $$\bigtriangleup$$ ABC whose vertices are $$A(7,-3), B(5,3)$$ and $$C(3,-1)$$ are

The mid point of the segment joining $$(2a, 4)$$ and $$(-2, 2b)$$ is $$(1, 2a+1)$$, then value of b is 

Determine the area of the triangle whose vertices are $$\displaystyle \left( \frac { 1 }{ 2 } ,\frac { -1 }{ 2 }  \right) ,\left( 2,\frac { -1 }{ 2 }  \right) $$ and $$\displaystyle \left( 2,\frac { \sqrt { 3 } -1 }{ 2 }  \right) $$.

If (2, 1), (-1, -2), (3, 3) are midpoints of sides BC, CA, AB of $$\displaystyle \Delta ABC$$, find the equation of AB. (A) x-y=1/2 (13) x+y= 1 (C) x-y=9 (D) x=y