Jitender Gupta and Divya Malik Solutions for Exercise 2: ARCHIVES (Last 8 Years)

$P\left(1, -2\right)$ is a point on the line segment joining $A\left(3, -6\right)$ and $B\left(x, y\right)$ such that $AP:PB$ is equal to $2:3$. Find the coordinates of $B$.

Calculate the ratio, in which the line joining $\mathrm{A}\left(-4,2\right) \mathrm{and} \mathrm{B}\left(3,6\right)$ is divided by $\mathrm{P}\left(\mathrm{x},3\right)$. Also find $\mathrm{x}$.

Calculate the ratio, in which the line joining $\mathrm{A}\left(-4,2\right) \mathrm{and} \mathrm{B}\left(3,6\right)$ is divided by $\mathrm{P}\left(\mathrm{x},3\right)$. Also find length of $\mathrm{AP}$.

$AB$ is a diameter of a circle with centre $C (-2, 5)$ and $A (3,- 7).$ Find the length of radius $AC$.

Given a line segment $\mathrm{AB}$ joining the points $\mathrm{A} (-4,6)$ and $\mathrm{B}(8,- 3)$. Find the ratio in which $\mathrm{AB}$ is divided by the $\mathrm{Y}-$axis.

Given a line segment $AB$ joining the points $A (-4,6)$ and $B(8,- 3)$. Find the ratio in which $AB$ is divided by the $Y$-axis and the coordinates of the point of intersection.

Given a line segment $AB$ joining the points $A (-4,6)$ and $B(8,- 3)$. Find the length of $AB.$

$ABC$ is a triangle and $G(4, 3)$ is the centroid of the triangle. If $A (1, 3), B(4, b)$ and $C(a, 1)$, then find $a$ and $b$. Find the length of side $BC$.