H K Dass, Rama Verma and, Bhagwat Swarup Sharma Solutions for Chapter: Co-Ordinate Geometry, Exercise 3: EXERCISE

If the centroid of the triangle, whose vertices are $(-4, 6), (2, -2)$ and $(2, 5)$ is $\left(x, y\right)$, then find the value of $x+y$.

Find the third vertex of a triangle, if two of its vertices are at $(-3, 1)$ and$(0, -2)$ and the centroid is at the origin.

Find the lengths of the medians of the triangle whose vertices are $(1, -1), (0, 4)$ and $(-5, 3)$

Find the centroid of the triangle formed by the straight lines $x-2y=0$, $x+y=3$ and $2x+y+4=0$.

Show that the middle point of the hypotenuse of a right-angled triangle is equidistant from the vertices.

Find the co-ordinates of the incentre of the triangle, whose vertices are $(0, 6)$, $(8, 12)$ and $(8, 0)$.