O P Malhotra, S K Gupta and, Anubhuti Gangal Solutions for Exercise 4: Exercise

Find the radius of the circle whose centre is at $\left(2,0\right)$ and which passes through $\left(7,-12\right)$.

Find the lengths of the sides of the triangle whose vertices are $A\left(3, 4\right), B\left(2, -1\right)$ and $C\left(4, -6\right)$.

Find the coordinates of the points on the $x$-axis which are at a distance of $10$ units from the point $\left(-4, 8\right)$.

Find the value of $p$ for which the points $\left(-1, 3\right), \left(2, p\right)$ and $\left(5, -1\right)$ are collinear.

Find the value of $\mathrm{x}$ such that $\mathrm{AB}=\mathrm{BC}$, where the coordinates of $\mathrm{A}, \mathrm{B}$ and $C$ are $\left(-5, 2\right), \left(1, -2\right)$ and $\left(x, 4\right)$ respectively.

The point $P\left(2, -5\right)$ is mapped onto point $P\text{'}$ on reflection in the $x$-axis and $Q\left(3, 7\right)$ is mapped onto the point $Q\text{'}$ on reflection in the origin. Find the length $PQ$ and $P\text{'}Q\text{'}$.

Points $A\left(5, 1\right)$ is the centre of a circle with radius $13$ units. $AB$ is perpendicular to the chord $PQ$. $B$ is $\left(2, -3\right)$. Calculate the length of  $AB$.

Points $A\left(5, 1\right)$ is the centre of a circle with radius $13$ units. $AB$ is perpendicular to the chord $PQ$. $B$ is $\left(2, -3\right)$. Calculate the length of  $PB$.