Tamil Nadu Board Solutions for Chapter: Coordinate Geometry, Exercise 13: Exercise

Find the centroid of the triangle whose vertices are $(2,-4),(-3,-7)$ and $(7,2)$.

Find the centroid of the triangle whose vertices are $(-5,-5),(1,-4)$and $(-4,-2)$.

If the centroid of a triangle is at $(4,-2)$ and two of its vertices are$(3,-2)$ and $(5,2)$, then find the third vertex of the triangle.

The vertices of a triangle are $(1,2), (h,-3)$ and $(-4, k)$. If the centroid of the triangle is at the point $(5,-1)$ then find the value of $\sqrt{(h+k{)}^2+(h+3k{)}^2}$.

Orthocentre and centroid of a triangle are $A(-3,5)$and $B(3,3)$ respectively. If $C$ is the circumcentre and $AC$ is the diameter of this circle, then find the radius of the circle.

$ABC$ is a triangle whose vertices are $\mathrm{A}(3,4), \mathrm{B}(-2,-1)$ and $\mathrm{C}(5,3)$. If $G$ is the centroid and $BDCG$ is a parallelogram then find the coordinates of the vertex $D$.

If $\left(\frac{3}{2},5\right) \left(7,\frac{-9}{2}\right) \left(\frac{13}{2},\frac{-13}{2}\right)$ are mid points of the sides of a triangle, then find the centroid of the triangle.

Show that the following points $A\left(3, 1\right), B\left(6, 4\right)$ and $C\left(8, 6\right)$ lies on a straight line.