Final answer:
To partition segment AC internally and externally in the ratio of 3 to 2, we can divide segment AC into five equal parts. This gives us segment AB of length 0.6 units and segment BD of length 0.4 units.
Step-by-step explanation:
To partition segment AC in the ratio 3 to 2, we divide the segment into five equal parts. Starting from point A, we count three parts and mark the point as B. This gives us segment AB. To find the length of AB, we can use a proportion: 1/5 = AB/AC. Solving for AB, we get AB = (3/5)AC. The length of AC is 1 unit, so the length of AB is (3/5)(1) = 0.6 units.
To find the length of BD, we count two parts externally from point C and mark the point as D. This gives us segment CD. Again, we can use a proportion: 1/5 = BD/CD. Solving for BD, we get BD = (2/5)CD. The length of CD is 1 unit, so the length of BD is (2/5)(1) = 0.4 units.