Section Formula

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

Find the centroid of the triangle whose veritices are $A\left(6, -1\right), B\left(8, 3\right)$ and $C\left(10, -5\right)$.

What are the coordinates of $B$ if point $P\left(-2, 3\right)$ divides the line segment joining $A\left(-3, 5\right)$ and $B$ internally in the ratio $1:6$?

In what ratio does the point $P\left(-2 ,4\right)$ divide the line segment joining the points $A\left(-3, 6\right)$ and $B\left(1, -2\right)$ internally?

Find the coordinates of the point which divides the line segment joining the points $\left(3, 5\right)$ and $\left(8, -10\right)$ internally in the ratio $3:2$.

Find the points of trisection of the line segment joining $\left(-2, -1\right)$ and $\left(4, 8\right)$.

The mid-points of the sides of a triangle are $\left(5, 1\right), \left(3, -5\right)$ and $\left(-5, -1\right)$. Find the coordinates of the vertices of the triangle.

Find the points which divide the line segment joining $A\left(-11, 4\right)$ and $B\left(9, 8\right)$ into four equal parts.

If $\left(x, 3\right), \left(6, y\right), \left(8, 2\right)$ and $\left(9, 4\right)$ are the vertices of a parallelogram taken in order, then find the value of $x$ and $y$.

The point $\left(3, -4\right)$ is the centre of a circle. If $AB$ is a diameter of the circle and $B$ is $\left(5, -6\right)$, find the coordinates of $A$.

In what ratio does the $y-$axis divide the line joining the points$(-5,1)$ and $\left(2,3\right)$ internally

If the coordinates of the midpoints of the sides $AB, BC$ and $CA$ of a triangle are $(3,4), (1,1)$ and $(2,-3)$respectively, then the vertices $A$ and $B$ of the triangle are

The ratio in which the $\mathrm{x}-$axis divides the line segment joining the points $(6,4)$ and$(1,-7)$ is

The ratio in which the $x-$axis divides the line segment joining the points $A\left(a_1\right.b_1)$ and $B\left(a_2,b_2\right)$ is

In what ratio does the point $Q(1,6)$ divides the line segment joining the points $P(2,7)$ and $R(-2,3)$?

The coordinates of the point $C$ dividing the line segment joining the points $P(2,4)$ and $Q(5,7)$internally in the ratio $2:1$ is