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

`(x,y)=((7)/(5),(39)/(5))`

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=
`((m_1x_2+m_2x_1)/(m_1+m_2),(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)=((3\cdot 3+2\cdot (-1))/(3+2),(3\cdot 9+2\cdot 6)/(3+2))`

`\Rightarrow (x,y)=((9-2)/(5),(27+12)/(5)`

`\Rightarrow (x,y)=((7)/(5),(39)/(5))`

Hence, required coordinates are:
`(x,y)=((7)/(5),(39)/(5))`