Mahabir Singh Solutions for Chapter: Coordinate Geometry, Exercise 1: MATHEMATICAL REASONING

Three points A $(1,-2)$, B $\left(\mathrm{3,4}\right)$ and C $\left(\mathrm{4,7}\right)$ form

The coordinates of the mid-points of the sides of a triangle are $\left(4,2\right),\left(3,3\right)$ and $(2,2)$. What will be the coordinates of the centroid of the triangle?

Area of quadrilateral formed by the vertices $\left(-1,6\right),\left(-3,-9\right),(5,-8)$ and $(3,9)$ is _____ (sq. units)

The vertices of a $∆$ABC are A $(2,1)$, B $(6,-2)$, C $(8,9)$. If AD is angle bisector, where D meets on BC, then coordinates of D are _____

The coordinates of the third vertex of an equilateral triangle whose two vertices are at $\left(3,4\right),(-2,3)$ are _____

In what ratio is the line segment joining the points $(-3,2)$ and $(6,1)$
Is divided by $y$-axis?

Find the coordinates of the point on $x$-axis which are equidistant from the points $\left(-3,4\right)$ and $(2,5)$

If the centroid of the triangle formed by the points $\left(a,b\right),(b,c)$ and
$(c,a)$ is at the origin, then $a^3+b^3+c^3=$