Question

Find the exact coordinates of point E.

Answer 1

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.

$x = \dfrac{mx_{2}+nx_{1}}{m+n}\\y = \dfrac{my_{2}+ny_{1}}{m+n}$

Where $(x,y)$ 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  

$x_{1} = -3\\x_{2} = 5\\y_{1} = 8\\y_{2} = 2$

Putting the given values in above formula :

x-co-ordinate of F:

$x = \dfrac{5 \times 4 + (-3 \times 1)}{4+1}\\\Rightarrow \dfrac{17}{5}\\\Rightarrow x = 3.4$

y-co-ordinate of F:

$y = \dfrac{4 \times 2 + 1 \times 8}{4+1}\\\Rightarrow \dfrac{16}{5}\\\Rightarrow y = 3.2$

So, answer is $E(3.4,3.2)$.