Neha Tyagi and Amit Rastogi Solutions for Chapter: Coordinate Geometry, Exercise 3: Exercise

If $\left(a, b\right)$ is the mid-point of the line segment joining the points $A\left(10, -6\right), B\left(k, 4\right)$ and $a-2b=18,$ then find the value of $k$ and the distance $AB.$

If the centre of a circle is $\left(2a, a-7\right)$, then find the value of $a$, if the circle passes through the point $\left(11, -9\right)$ and has diameter $10\sqrt{2}$ units.

The line segment joining the points $A\left(3, 2\right)$ and $B\left(5, 1\right)$ is divided at the point $P$ in the ratio $1:2$ and it lies on the line $3x-18y+k=0$. Find the value of $k$.

If $D(-\frac{1}{2},\frac{5}{2})$$,E(7,3)$ and $F(\frac{7}{2},\frac{7}{2})$ are the mid-points of sides of $\Delta ABC$, then find the area of the $\Delta ABC$.

If the points $A\left(2, 9\right), B \left(a, 5\right)$ and $C\left(5, 5\right)$ are the vertices of a $∆ABC$right angled at B, then find the values of $a$ and hence the area of $∆ABC$.

Find the coordinates of the point `R` on the line segment joining the points $P\left(-1, 3\right)$ and $Q\left(2, 5\right)$ such that $PR=\frac{3}{5}PQ$.

Find the values of k, if the points $A\left(k+1, 2k\right),B\left(3k, 2k + 3\right)$ and $C\left(5k -1, 5k\right)$ are collinear.

Find the ratio in which the line $2x+3y-5=0$ divides the line segment joining the points $\left(8, -9\right)$ and $\left(2, 1\right)$. Also, find the coordinates of the point of division.