R. D. Sharma Solutions for Chapter: Co-Ordinate Geometry, Exercise 3: EXERCISE 6.3

Find the points of trisection of the line segment joining the points:

$(3, -2)$ and $(-3, -4)$

Find the points of trisection of the line segment joining the points:

$(2, -2)$ and $(-7, 4)$

Find the ratio in which the line segment joining $(-2,-3)$ and $(5,6)$ is divided by $y$-axis. Also, find the coordinates of the point of division in each case. Let the sum of the ratios be $f$, the sum of coordinates of the point of division be $g$ and if $h=-gf$, find $h$.

Show that $\mathrm{A}(-3,2), \mathrm{B}(-5,-5), \mathrm{C}(2,-3)$ and $\mathrm{D}(4,4)$ are the vertices of a rhombus.

Find the lengths of the medians of a $△\mathrm{ABC}$ having vertices at $\mathrm{A}(0,-1), \mathrm{B}(2,1)$ and $\mathrm{C}(0,3).$

If $\mathrm{P}(4,\mathrm{m})$ divides the line segment joining the points $\mathrm{A}(2,3)$ and $\mathrm{B}(6,-3)$ in the ratio $\mathrm{\lambda }:1$ then find $\mathrm{m}$.

Find the coordinates of the points which divide the line segment joining the points $(-4, 0)$ and $(0, 6)$ in four equal parts.

The line segment joining the points $\mathrm{P}(3,3) \mathrm{and} \mathrm{Q}(6,-6)$ is trisected at the points $A$ and $B$ such that $A$ is nearer to $P$. If $A$ also lies on the line given by $2x+y+k=0,$ find the value of $k$.