Question

Find the exact coordinates of point E.

Answer 1

is the correct answer.

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 = (mx_(2)+nx_(1))/(m+n)\\y = (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 = (5 * 4 + (-3 * 1))/(4+1)\\\Rightarrow (17)/(5)\\\Rightarrow x = 3.4`

y-co-ordinate of F:

`y = (4 * 2 + 1 * 8)/(4+1)\\\Rightarrow (16)/(5)\\\Rightarrow y = 3.2`

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