Question

Which point will divide segment AB into a 2:1 ratio.O (6,2)O (5.2.5)O (7.1.5) O (8.1) I am confused on this can you help me understand

Answer 1

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given points

`\begin{gathered} A(2,4) \\ B(8,1) \end{gathered}`

STEP 2: The given ratio is 2:1

`m=2,n=1`

STEP 3: Write the formula to use

`\begin{gathered} ((mx_2+nx_1)/(m+n),(my_2+ny_1)/(m+n)) \\ \end{gathered}`

By substitution, we have:

`\begin{gathered} ((2(8)+1(2))/(2+1),(2(1)+1(4))/(2+1) \\ \\ =((16+2)/(3),(2+4)/(3)) \\ =((18)/(3),(6)/(3)) \\ =(6,2) \end{gathered}`

Hence, the answer is:

`(6,2)`