Coordinate Geom...

If point P divides the line joining the points $$(5, 0)$$ and $$(0, 4)$$ in the ratio $$2 : 3$$ internally, then the $$x$$-coordinate of $$P$$ is

If mid point of the line segment joining $$(2a, 4)$$ and $$(-2, 3b)$$ is  $$(1, 2a + 1)$$, then the values of  $$a$$ and $$b$$ are given by

The coordinates of $$A$$ and $$B$$ are $$(1, 2) $$ and $$(2, 3)$$. Find the coordinates of $$R $$, so that  $$\displaystyle \frac{AR}{RB} = \frac{4}{3}$$.

The co-ordinates of a point $$R$$ which divides the line joining  $$A(-3, 3)$$ and $$B(2, - 7)$$ internally in the ratio $$2 : 3$$ are

$$M$$ is the midpoint of the straight line $$PQ$$. If $$P$$ is  $$(-2,  9)$$  and $$M$$ is (4, 3), find the coordinates of $$Q.$$

The Point $$A$$ on x-axis and point $$B$$ on y-axis and the mid-point of the line segment AB is shown in the figure is $$(4 - 3)$$. Then, the co-ordinates of A and B are

If the line joining points $$(5, -6)$$ and $$(9, 8)$$ divided by a point R internally in $$5 : 6$$ ratio, then R =

If (2, 1), (4, 5), (-1, - 3) are the mid points of the sides of a triangle, then the co-ordinates of its vertices are

The diagram is on a Cartesian plane.
If the midpoints of PQ and RS are the same, the coordinates of S are:

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