NCERT Solutions · Class 10 Mathematics Coordinate Geometry

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

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

To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1m each. $\displaystyle 100$ flower pots have been placed at a distance of 1m from each other along AD, as shown in Fig. 7.12. Niharika runs $\displaystyle \frac{1}{4}$ th the distance AD on the 2nd line and posts a green flag. Preet runs $\displaystyle \frac{1}{5}$ 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 $\displaystyle (-3, 10)$ and $\displaystyle (6, -8)$ is divided by $\displaystyle (-1, 6)$.

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

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

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

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

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

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