Question

Point B splits a segment AC with ratio AB:BC=2:1. Point D splits a segment AB with the ratio AD:DB=3:2. What is the ratio for AD:DC?

Answer 1

Answer:

The ratio for AD:DC is 2:3

Step-by-step explanation:

The given information are;

The ratio by which point B splits AC as AB:BC = 2:1

The ratio by which point D splits AB as AD:DB = 3:2

Therefore, we have;

The fraction of AC that is equal to AB is given as follows;

AB = 2/(2 + 1) × AC = 2/3 × AC

AB = 2/3 × AC

Similarly

BC = 1/3 × AC

Also the fraction of AB that is equal to AD is given as follows;

AD = 3/(3 + 2) × AB = 3/5 × AB

AD = 3/5 × AB

Therefore, the fraction of AC that is equal to AD is given as follows;

AD = 3/5 × AB = 3/5 × 2/3 × AC = 2/5 × AC

Therefore, DC = (1 - 2/5) × AC = 3/5 × AC

Which gives the ration of AD to DC or AD:DC as being;

AD:DC = 2/5 × AC : 3/5 × AC  = 2/5:3/5 = 2:3

The ratio for AD:DC = 2:3.