Jitender Gupta and Divya Malik Solutions for Exercise 1: CHAPTER EXERCISE

Find the centroid of a triangle, whose vertices are $\left(3, -5\right), \left(-7, 4\right)$ and $\left(10, -2\right)$.

Two vertices of a triangle are $\left(-1, 4\right)$ and $\left(5, 2\right).$ If the centroid is $\left(0, -3\right)$, then find the third vertex.

The centroid of a triangle is the point $\left(6, -1\right)$. If two vertices are $\left(3, 4\right)$ and $\left(-2, 5\right)$, then find third vertex.

Two vertices of a triangle are $\left(3, -5\right)$ and $\left(-7, 4\right).$ If its centroid is $\left(2, -1\right)$, then find the third vertex.

The line segment joining $A\left(-1,\frac{5}{3}\right)$ and $B(a,5)$ is divided in the ratio $1:3$ at $P,$ the point where the line segment $AB$ intersects$Y-axis$. Calculate the value of a and coordinates of $P.$

The line segment joining $A (-2, 3)$ and $B (m, 4)$ is divided in the ratio $1 : 4$ at $P$, the point where the line segment $AB$ intersects $Y-$axis. Calculate the value of $m$.

If $A(-4,3)$ and $B(8,-6)$, find the length of $AB.$  [Write your answer excluding units]

The line joining $P(-4,5)$ and $Q(3,2)$ intersect the $Y$axis at $R$. $PM$ and $QN$ are perpendicular from $P$ and $Q$on the X-axis. Find the ratio $PR:PQ.$