The end points of a line segment are (2, 3), (4, 5). Find the slope of the line segment.

If vec(a)=4vec(i)-3hat(j) " and " vec(b)=-2hat(i)+5hat(j) are the position vectors of the points A and B respectively, find (i) the position vector of the middle point of the line-segment bar(AB) , (ii) the position vectors of the points of trisection of the line-segment bar(AB) .

Some points are plotted on a plane such that any three of them are non collinear. Each point is joined with all remaining points by line segments. Find the number of points if the number of line segments are 10.

Show that the mid-point of the line segment joining the points (5, 7) and (3, 9) is also the mid-point of the line segment joining the points (8, 6) and (0, 10).

The coordinates of the points A,B,C and D are (-2,3), (8,9), (0,4) and (3,0) respectively . Find the ratio in which the line -segment overline(AB) is divided by the line -segment overline(CD) .

Prove that the points (-4,-5) ,(9,8)and the mid-point of the line-segment joining the point (2,1) and (6,5) are on the same straight line

Find the slope of a line, which passes through the origin, and the mid-point of the line segment joining the points P (0,- 4) and B (8,0).

A point with y-coordinate 5 lies on the line-segment joining the points ( 1 , 4 , -3) and (4 , 7 , - 6) , find the coordinates of the point .

Find the coordinates of the midpoint of the line segment intersected by the axes of the straight line 4x + 3y + 12 = 0.

At any point (x,y) of a curve, the slope of the tangent is twice the slope of the line segment joining the point of contact to the point(-4, -3).Find the equation of the curve given that it passes through (-2, 1).

Show that the line -segment joining the points (8,3),(-2,7) and the line -segment joining (11,-2),(-5,12) bisect each other .