AB is a line 6.4 cm in length it is divided internally at X and externally at Y in the ratio 5 : 3 calculate the lengths of the segments and show that, 1/AX +1/AY = 2/AB
Answers
Your answer is given below -:::
Step-by-step explanation:
Since the point C divided the line AB internally then point C is between A and B.
This means that we have lengths :
AC and BC
The ratio of the division is given by :
AC : BC = 3:5
We can rewrite this as follows:
AC/BC = 3/5
Eliminating the denominators we have.;
Hence we have that :
5AC = 3BC
Now AB = sum of the ratios (5 + 3) = 8
AC : AB = 3 : 8
AC/AB = 3/8
8AC = 3AB.
Step-by-step explanation:
STEPS OF CONSTRUCTION:
1.Draw line segment of length AB=8cm.
2. Draw any Ray AX making acute ∠BAX with AB
3. Draw a parallel to BY parallel to AX by making∠ABY=∠BAX.
4. Make 3 points A1 ,A2 ,AA on AX & 4 points B1 ,B2,B3 ,B4 on BY such that
AA1=A1 A2 =A2 A3 =BB1=B1 B2
=B2 B 3
=B3 B4
5. Join A3 B4
. Then it intersect AB at a point P.
Thus P is the point of dividing AB internally in the ratio 3:4.