Manipur Board Solutions for Chapter: Coordinate Geometry, Exercise 1: EXERCISE 11.1

In what ratio is the line segment joining the points $(-2,-3)$ and $(3,7)$ divided by the y- axis? Also, find the co-ordinates of the point of division.

If a vertex of a triangle be $(1, 1)$ and the middle points of the sides through it be $(-2,3)$ and $(5, 2)$, find the other vertices.

Show that the points $(3,-2), (4,0), (6,-3)$ and $(5,-5)$ are the vertices of a parallelogram taken in order.

Show that the four points $(1 ,2), (3,0), (7,4)$ and $(5,6)$ taken in order are the angular points of a rectangle.

Determine the ratio in which the point $(10, m)$ divides the join of $A(5, 2)$and $B(17, 14)$. Also, find the value of $m$.

Find the centroid of $∆ABC$ whose vertices are $A(-1, 0), B(5, -2)$ and $C(8, 2)$

If the points $A(a, -11), B(5,b), C(2,15)$ and $D(1, 1)$ taken in order are the vertices of a parallelogram $ABCD$, find the values of $a$ and $b$.

Three vertices of a rectangle are the points $(3, 4)$, $(-1, 2)$ and $(2, -4)$; what are the co- ordinates of the fourth vertex.