Exercise 7.2

To conduct Sports Day activities, in your rectangular shaped school ground $\mathrm{}\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$, lines have been drawn with chalk powder at a distance of $\mathrm{}1\mathrm{m}$ each. $100$ flower pots have been placed at a distance of $\mathrm{}1\mathrm{}\mathrm{m}\mathrm{}$ from each other along $\mathrm{}\mathrm{A}\mathrm{D}$, as shown in Fig. Niharika runs $\frac{1}{4}th$ the distance $\mathrm{}\mathrm{A}\mathrm{D}\mathrm{}$ on the $2^{\mathrm{n}\mathrm{d}}\mathrm{}$ line and posts a green flag. Preet runs $\frac{1}{5}\mathrm{t}\mathrm{h}\mathrm{}$ the distance $\mathrm{}\mathrm{A}\mathrm{D}$ on the eighth line and posts a red flag. What is the distance between both the flags? If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag?

Find the ratio in which the line segment joining the points $\left(-3,\mathrm{}10\right)$ and $\left(6,\mathrm{}-8\right)$ is divided by $\left(-1,\mathrm{}6\right)$.

Find the ratio in which the line segment joining $\mathrm{}\mathrm{A}\left(1,\mathrm{}-5\right)$ and $\mathrm{}\mathrm{B}\left(-4,\mathrm{}5\right)$ is divided by the $x-$axis. Also find the coordinates of the point of division.

If $\left(1,2\right), \left(4,y\right), \left(x,6\right)$ and $\left(3,\mathrm{}5\right)$ are the vertices of a parallelogram taken in order, find $x$ and $y$.

Find the coordinates of a point $\mathrm{}\mathrm{A}$, where $\mathrm{}\mathrm{A}\mathrm{B}$ is the diameter of a circle whose centre is $\left(2,\mathrm{}-3\right)$ and $\mathrm{}\mathrm{B}$ is $\left(1,\mathrm{}4\right)$.

If $\mathrm{}\mathrm{A}\mathrm{}$ and $\mathrm{}\mathrm{B}$ are $\left(-2,\mathrm{}-2\right)$ and $\left(2,\mathrm{}-4\right)$, respectively, find the coordinates of $\mathrm{}\mathrm{P}$ such that $\mathrm{A}\mathrm{P}=\frac{3}{7}\mathrm{A}\mathrm{B}$ and $\mathrm{}\mathrm{P}$ lies on the line segment $\mathrm{}\mathrm{A}\mathrm{B}$.

Find the coordinates of the points which divide the line segment joining $\mathrm{}\mathrm{A}\left(-2,\mathrm{}2\right)$ and $\mathrm{}\mathrm{B}\left(2,\mathrm{}8\right)$ into four equal parts.

Find the area of a rhombus if its vertices are $\left(3,0\right), \left(4,5\right), \left(-1,4\right)$ and $\left(-2,\mathrm{}-1\right)$ taken in order.
[Hint: Area of a rhombus $=\frac{1}{2}$(product of its diagonals)]