Question

Point b lies on the segment ac . Find the length of the segment ac, if ab=7.8 cm, bc=25mm. How many different solutions can this problem have? What if we said that point b lies on the line defined by points a and c?

Answer 1

Given that B lies on segment AC and AB=7.8cm , BC = 25mm

Let us convert AB to mm by multiplying with 10 that is AB = 78mm

There are totally 3 possible  ways for B lying on segment AC.

Solution 1:- B lies in between A and C,

Then AC = AB+BC

               =78+25 = 103 mm

Solution 2:- B lies to the right of C like ACB.

Then AB = AC+CB

         78 = AC+25

         AC = 78-25 = 53mm

Solution 3:- B lies to the left of A like BAC.

Then BC = BA+AC

          25 = 78+AC

Since AC cannot be negative, this way is not possible.

Hence there are only 2 solutions possible.

If we are given that B lies on line joining A and C, then definitely B should lie between A and C.  That means nothing but solution 1. So only one solution is possible in this case.