R K Bansal Solutions for Exercise 1: EXERCISE

Calculate the ratio in which the line joining $\mathrm{A}(-4, 2)$ and $\mathrm{B}(3, 6)$ is divided by point $\mathrm{P}(\mathrm{x}, 3).$ Also, find length of$\mathrm{AP}.$
 

The line joining the points $(2, 1)$ and $(5, -8)$ is trisected at the points $\mathrm{P}$ and $\mathrm{Q}.$ If point $\mathrm{P}$ lies on the line $2\mathrm{x} - \mathrm{y} + \mathrm{k} = 0,$ find the value of $\mathrm{k}.$ Also, find the co-ordinates of point $\mathrm{Q}.$
 

Find the image of the point $\mathrm{A}(5, -3)$ under reflection in the point $\mathrm{P}(-1, 3).$
 

$\mathrm{M}$ is the midpoint of the line segment joining the points $\mathrm{A}(0, 4)$ and $\mathrm{B}(6, 0).$ $\mathrm{M}$ also divides the line segment $\mathrm{OP}$ in the ratio $1 :3.$ Find coordinates of $\mathrm{M}$.

$\mathrm{M}$ is the midpoint of the line segment joining the points $\mathrm{A}(0, 4)$ and $\mathrm{B}(6, 0).$ $\mathrm{M}$ also divides the line segment $\mathrm{OP}$ in the ratio $1 :3.$ Find coordinates of $\mathrm{P}$.

$\mathrm{M}$ is the midpoint of the line segment joining the points $\mathrm{A}(0, 4)$ and $\mathrm{B}(6, 0).$ $\mathrm{M}$ also divides the line segment $\mathrm{OP}$ in the ratio $1 :3.$ Find length of $\mathrm{BP}$.

$\mathrm{A}(-4, 2), \mathrm{B}(0, 2)$ and $\mathrm{C}(-2, -4)$ are vertices of a triangle $\mathrm{ABC}. \mathrm{P}, \mathrm{Q}$ and $\mathrm{R}$ are midpoints of sides $\mathrm{BC}, \mathrm{CA}$ and $\mathrm{AB}$ respectively. Show that the centroid of $△\mathrm{PQR}$ is the same as the centroid of $△\mathrm{ABC}.$

$\mathrm{A}(3, 1), \mathrm{B}(y, 4)$ and $\mathrm{C}(1, x)$ are vertices of triangle $\mathrm{ABC}$ and $\mathrm{G}(3, 4)$ is its centroid. Find the values of $x$ and $y.$ Also, find the length of side $\mathrm{BC}.$