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

SOLUTION

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

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

By substitution, we have:

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

Hence, the answer is:

$(6,2)$