Exercise 7.2

Find the coordinates of the point which divides the join of $(-1, 7)$ and $(4, -3)$ in the ratio $2 : 3$.

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

Find the coordinates of the points of trisection of the line segment joining $(4,-1)$ and $(-2,-3)$.

To conduct Sports Day activities, in your rectangular‑shaped school ground $ABCD$, lines have been drawn with chalk powder at a distance of $1\text{ m}$ each. $100$ flower pots have been placed at a distance of $1\text{ m}$ from each other along $AD$, as shown in Fig. 7.12.

Niharika runs $\dfrac{4}{5}$ of the distance $AD$ on the $2^{\text{nd}}$ line and posts a green flag.

Preet runs $\dfrac{1}{5}$ of the distance $AD$ on the $8^{\text{th}}$ 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 $(-3,\,10)$ and $(6,\,-8)$ is divided by $(-1,\,6)$.

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

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

Find the coordinates of a point $A$, where $AB$ is the diameter of a circle whose centre is $(2, -3)$ and $B$ is $(1, 4)$.

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

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