Point C is the midpoint of ⎯⎯⎯⎯⎯⎯⎯⎯ A B ¯ , point D is the midpoint of ⎯⎯⎯⎯⎯⎯⎯⎯ A C ¯ , point E is the midpoint of ⎯⎯⎯⎯⎯⎯⎯⎯⎯ A D ¯ , and point F is the midpoint of ⎯⎯⎯⎯⎯⎯⎯⎯⎯ A E ¯ . If =3 A F = 3 , what is the number of units in the length of ⎯⎯⎯⎯⎯⎯⎯⎯ A B ¯ ?

48 units

Step-by-step explanation:

Point C is the midpoint o A B, point D is the midpoint of A C, point E is the midpoint of AD, and point F is the midpoint of AE. If A F = 3, what is the number of units in the length of AB.

Solution:

AE = 2* distance from A to F (F is at the midpoint of AB)

AD = 2 * AE (E is at the midpoint of AB)

AC = 2 * AD (D is at the midpoint of AB)

AB = 2 * AC (C is at the midpoint of AB)

Therefore since AB = 2 * AC

AB = 2(AC) = 2(2AD) = 4(AD)

AB = 4(AD) = 4(2 * AE)

AB = 8 * AE = 8(2 * A F)

AB = 16 * distance from A to F

To find the value of AB, when A F = 3, we substitute distance from A to F = 3;

AB = 16 * A F = 16 * 3 = 48 units

inverse operation of addition