M L Aggarwal Solutions for Exercise 3: Chapter Test

The centre of a circle is $\left(\alpha +2, \alpha -5\right)$. Find the value of $\alpha$, given that the circle passes through the points $\left(2, -2\right)$ and $\left(8, -2\right)$.

The ends of a diameter of a circle have the coordinates $\left(3, 0\right)$ and $\left(-5, 6\right)$. $PQ$ is another diameter where $Q$ has the coordinates $\left(-1, -2\right)$. Find the coordinates of $P$ and the radius of the circle.

Find the ratio in which the point $P\left(-3, p\right)$ divides the line segment joining the points $\left(-5, -4\right)$ and $\left(-2, 3\right)$. Hence, find the value of $p$.

In what ratio is the line joining the points $\left(4, 2\right)$ and $\left(3, -5\right)$ divided by the $x$-axis? Also find the coordinates of the point of division.

Given $O\left(0, 0\right), P\left(1, 2\right), S\left(-3, 0\right)$. $P$ divides $OQ$ in the ratio$2:3$ and $OPRS$ is a parallelogram. Find: the coordinates of $Q$. 

Given $\mathrm{O}(0, 0), P(1, 2), S(-3, 0)$. $P$ divides $OQ$ in the ratio $2:3$ and $OPRS$ is a parallelogram. Find:

the coordinates of $R$.

Given $O\left(0, 0\right), P\left(1, 2\right), S\left(-3, 0\right)$. $P$ divides $OQ$ in the ratio $2:3$ and $OPRS$ is a parallelogram. Find: the ratio in which $RQ$ is divided by the $y$-axis.

If $A\left(5, -1\right), B\left(-3, -2\right)$ and $C\left(-1, 8\right)$ are the vertices of a triangle $ABC$, find the length of the median through $A$ and the coordinates of the centroid of triangle $ABC$.