Question

Point E is located at (−1, 6) and point F is located at (3, 9)


What are the coordinates of the point that partitions the directed line segment EF¯¯¯¯¯ in a 3:2 ratio?


Enter your answer, as decimals, in the boxes.

Answer 1

Answer:

$(x,y)=(\frac{7}{5},\frac{39}{5})$

Step-by-step explanation:

We have given:  

E is (-1,6) and F is (3,9)

And ratios are 3:2

We will use the section formula to find the required coordinates:

section formula=$(\frac{m_1x_2+m_2x_1}{m_1+m_2},\frac{m_1y_2+m_2y_1}{m_1+m_2})$

Here,$m_1=3,m_2=2,x_1=-1,x_2=3,y_1=6,y_2=9$

On substituting the values in the formula we get:

$(x,y)=(\frac{3\cdot 3+2\cdot (-1)}{3+2},\frac{3\cdot 9+2\cdot 6}{3+2})$

$\Rightarrow (x,y)=(\frac{9-2}{5},\frac{27+12}{5}$

$\Rightarrow (x,y)=(\frac{7}{5},\frac{39}{5})$

Hence, required coordinates are:  $(x,y)=(\frac{7}{5},\frac{39}{5})$