Q. 44.2( 5 Votes )

The line segment joining A (2,3) and B(-3,5) is extended through each end by a length equal to its original length. Find the coordinates of the new ends.

Answer :


Let P and Q be the required new ends


Coordinates of P


Let AP = k


AB = AP = k


and PB = AP + AB = k + k = 2k



P divides AB externally in the ratio 1:2


Using the section formula for the external division, i.e.


…(i)


Here, m1 = 1, m2 = 2


(x1, y1) = (2, 3) and (x2, y2) = (-3, 5)


Putting the above values in the above formula, we get





x = 7, y = 1


Coordinates of P are (7, 1)


Coordinates of Q.


Q divides AB externally in the ratio 2:1


Again, Using the section formula for the external division, i.e.


…(i)


Here, m1 = 2, m2 = 1


(x1, y1) = (2, 3) and (x2, y2) = (-3, 5)


Putting the above values in the above formula, we get





Coordinates of Q are (-8, 7)


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