Question 5

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

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 $\dfrac{1}{4}\text{th}$ the distance $AD$ on the 2nd line and posts a green flag. Preet runs $\dfrac{1}{5}\text{th}$ the distance $AD$ 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 $(-3, 10)$ and $(6, -8)$ is divided by $(-1, 6)$.

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

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

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

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)]