Answer:
is the correct answer.
Step-by-step explanation:
We are given that co-ordinates of D is (-3,8) and F is (5,2).
For finding a point E on the line segment DF dividing it in a ratio 4:1, we can use segment formula.
[tex]x = \dfrac{mx_{2}+nx_{1}}{m+n}\\y = \dfrac{my_{2}+ny_{1}}{m+n}[/tex]
Where [tex](x,y)[/tex] is the co-ordinate of the point which
divides the line segment joining the points and in the ratio m:n.
As per the given values
[tex]x_{1} = -3\\x_{2} = 5\\y_{1} = 8\\y_{2} = 2[/tex]
Putting the given values in above formula :
x-co-ordinate of F:
[tex]x = \dfrac{5 \times 4 + (-3 \times 1)}{4+1}\\\Rightarrow \dfrac{17}{5}\\\Rightarrow x = 3.4[/tex]
y-co-ordinate of F:
[tex]y = \dfrac{4 \times 2 + 1 \times 8}{4+1}\\\Rightarrow \dfrac{16}{5}\\\Rightarrow y = 3.2[/tex]
So, answer is [tex]E(3.4,3.2)[/tex].
