K. C. Sinha Solutions for Chapter: Cartesian System of Rectangular Coordinates, Exercise 3: 1.3

The vertices of a triangle $ABC$ are $A\left(0,0\right), B\left(2,-1\right)$ and $C\left(9,2\right)$, find $\cos B$.

Find the ratio in which $\left(-8,3\right)$ divides the join of points $\left(2,-2\right)$ and $\left(-4,1\right)$.

Find the centroid and incentre of the triangle whose vertices are $\left(2,4\right),\left(6,4\right),\left(2,0\right)$.

The mid-points of the sides of a triangle are $\left(\frac{1}{2},0\right),\left(\frac{1}{2},\frac{1}{2}\right)$ and $\left(0,\frac{1}{2}\right)$. Find the coordinates of the incentre.

Find the area of the triangle whose vertices are $\left(a\cos \alpha ,b\sin \alpha \right),\left(a\cos \beta ,b\sin \beta \right),\left(a\cos \gamma ,b\sin \gamma \right).$

Find the area of the quadrilateral whose vertices are

$\left(-4,5\right),\left(0,7\right),\left(5,-5\right)$ and $\left(-4,-2\right)$

Find the area of the hexagon whose consecutive vertices are $\left(5,0\right),\left(4,2\right),\left(1,3\right),\left(-2,2\right),\left(-3,-1\right)$ and $\left(0,-4\right).$

The coordinates of the centroid of a triangle and those of two of its vertices are respectively $\left(\frac{2}{3},2\right),\left(2,3\right),\left(-1,2\right)$. Find the area of the triangle.