" 4.The mid-point of the line scgment joining the points "(x_(1),y_(1)),(x_(2),y_(2))" is "

Find the coordinates of the mid-point of the line joining the points (x_(1) , y_(1) ) and (x_(2), y_(2)) .

The points P divides the line - segment joining the points A(x_(1),y_(1))andB(x_(2),y_(2)) in the ratio m : n . If P lies on the line ax+by +c=0 , prove that, (m)/(n)=-(ax_(1)+by_(1)+c)/(ax_(2)+by_(2)+c) .

If M(alpha , beta , gamma ) is the mid point of the line segment joining the points A(x_(1),y_(1),z_(1)) and B then find B.

The coordinates of the point which divides the line segment joining the points (x_(1);y_(1)) and (x_(2);y_(2)) internally in the ratio m:n are given by (x=(mx_(2)+nx_(1))/(m+n);y=(my_(2)+ny_(1))/(m+n))

Show that the equation of the straight line joining the points (x_(1),y_(1))and(x_(2),y_(2)) can be expressed in the form (x-x_(2))(y-y_(1))=(x-x_(1))(y-y_(2)) .

Find the coordinates of the mid-point of the line joining the points (x_1, y_1) and (x_2, y_2).

If (1,(p)/(3)) is the mid-point of the line segment joining the points (2,0) and (0,(2)/(9)), then show that the line 5x+3y+2=0 passes through the point (-1,3p)

If the coordinates of the mid-point of the line segment joining the points (2, 1) and (1, - 3) is (x, y), then the relation between x and y can be best described by

The coordinates of any point on the line-segment joining the points ( x _(1) ,y_(1) , z_(1)) and (x_(2), y_(2),z_(2)) are ((x_(1)+kx_(2))/(k + 1),(y _(1) + ky_(2))/(k + 1),(z_(1)+kz_(2))/(k + 1)) , then the value of k will be _