Coordinate Geom...

A line intersects the $$y$$-axis and $$x$$-axis at the points $$P$$ and $$Q$$ respectively. If $$(2, 5)$$ is the mid-point of $$PQ$$, then the coordinates of $$P$$ and $$Q$$ are respectively

Plot $$(3, 0), (5, 0)$$ and $$(0, 4) $$ on cartesian plane. Name the figure formed by joining these points and find its area.

The point, which divides the line segment joining the points $$(7, 6)$$ and $$(3, 4)$$ in ratio $$1 : 2$$ internally, lies in the

The area of a triangle with vertices $$A (3, 0), B (7, 0)$$ and $$C (8, 4)$$ is

The points $$A (2, 9), B (a, 5)$$ and $$C (5, 5) $$ are the vertices of a triangle $$ABC$$ right angled at $$B$$. Find the values of  $$a$$ and hence the area of $$\Delta $$ $$ABC$$.

If $$P$$ $$(9a-  2, b)$$ divides line segment joining $$A$$ $$(3a + 1, -3)$$ and $$B$$ $$(8a, 5)$$ in the ratio $$3:1$$, find the values of $$a$$ and $$b.$$

Find the coordinates of the point $$R$$ on the line segment joining the points $$P (1, 3)$$ and $$Q (2, 5)$$ such that $$PR =\dfrac{3}{5}PQ$$.

The median from A meets BC at D. Find the coordinates of the point D.

Find the area of triangle having vertices $$A (6, 10), B (4, 5)$$ and $$C (3, 8)$$ .

If $$x-$$axis divide the line segment joining the points $$( 4, 6)$$ and $$(1,-7)$$ in ratio $$m:n$$, then the coordinates of the point of division is