Telangana Board Solutions for Chapter: Coordinate Geometry, Exercise 8: Try This

Let $\mathrm{A}(4, 2), \mathrm{B}(6, 5)$and $\mathrm{C}(1, 4)$be the vertices of $△\mathrm{ABC}$, $\mathrm{AD}$ is the median on $\mathrm{BC}$. Find the coordinates of the point $\mathrm{D}$.

Let $\mathrm{A}(4, 2), \mathrm{B}(6, 5)$and $\mathrm{C}(1, 4)$be the vertices of $△\mathrm{ABC}$, $\mathrm{AD}$ is the median on $\mathrm{BC}$. Find the coordinates of the point $\mathrm{P}$ on $\mathrm{AD}$ such that $\mathrm{AP}:\mathrm{PD}=2:1$.

Let $\mathrm{A}(4, 2), \mathrm{B}(6, 5)$and $\mathrm{C}(1, 4)$be the vertices of $△\mathrm{ABC}$. Find the coordinates of points $\mathrm{Q}$ and $\mathrm{R}$ on medians $\mathrm{BE}$ and $\mathrm{CF}$.

Let $\mathrm{A}(4, 2), \mathrm{B}(6, 5)$and $\mathrm{C}(1, 4)$be the vertices of $△\mathrm{ABC}$. Find the points which divide the line segment $\mathrm{BE}$ in the ratio $2:1$and also that divides the line segment $\mathrm{CF}$ in the ratio $2:1$.

Let $\mathrm{A}(4, 2), \mathrm{B}(6, 5)$and $\mathrm{C}(1, 4)$be the vertices of $△\mathrm{ABC}$. Justify that the point which divides each median in the ratio $2:1$ is the centroid of a triangle such that $\mathrm{AP}:\mathrm{PD}=2:1$.