𝐴𝐶 and 𝐷𝐹 are lines of length 18 units. Part a, the ratio 𝐴𝐵 to 𝐵𝐶 is two to seven. Mark the point 𝐵 on the line 𝐴𝐶 using a cross. Part b, the ratio 𝐷𝐸 to 𝐸𝐹 is one to three. Mark the point 𝐸 on the line 𝐷𝐹 using a cross.
Our ratio in part a is two to seven This means that we have a total of nine parts, as two plus seven is equal to nine. The length of the whole line 𝐴𝐶 was equal to 18 units. Therefore, we can calculate the length of one part of the ratio by dividing 18 by nine. 18 divided by nine is equal to two. This represents one part of the ratio. The length 𝐴𝐵 represented two parts. Therefore, we need to multiply two by two. This is equal to four. Therefore, 𝐴𝐵 has length four units. The length 𝐵𝐶 was represented by seven parts in the ratio. Therefore, we need to multiply seven by two. Seven multiplied by two is equal to 14. Therefore, the length on the line 𝐵𝐶 is 14 units. Point 𝐵 lies on the line as shown. It is four units from 𝐴 and 14 units from 𝐶.
We can now repeat this process for part b. This time the ratio of 𝐷𝐸 to 𝐸𝐹 was one to three. This means that our first step is to add one and three. This equals four. So we have four parts in total. Once again, we’re told that 𝐷𝐹 is length 18 units. This means that we need to divide 18 by four. 18 divided by four is equal to 4.5. This means that one part in this case is equal to 4.5 units. The length 𝐷𝐸 was equal to one part of the ratio and one multiplied by 4.5 is equal to 4.5. The length of 𝐷𝐸 well therefore be equal to 4.5 units.
The length 𝐸𝐹 was three parts of the ratio. We need to multiply three by 4.5. This is equal to 13.5. Therefore, the length 𝐸𝐹 is 13.5 units. We can, therefore, mark point 𝐸 using a cross 4.5 units from 𝐷 and 13.5 units from 𝐹. In both parts of the question, it is worth checking that our two lengths total 18. Four plus 14 is equal to 18, and 4.5 plus 13.5 is also equal to 18.