Question

Question #07155

Answer 1

C) 5.17, 7.33

Explanation:

We know if point (x,y) = divides `(x_1, y_1) and (x_2, y_2)` in the ratio of m:n, then the coordinates of (x,y) = `[mx_2+nx_1]/[m+n],[my_2+ny_1]/[m+n].`

Here point R divides E(4,8) and F(11,4) internally. Hence co-ordinates
of R say (x,y) =

`[1.11+5.4]/[1+5], [1.4+5.8]/[1+5]`

= `31/6 , 44/6`

= 5.1666, 7.33 = 5.17, 7.33

Answer 2

The answer is option `C=((5.17),(7.33))`

Explanation:

We try a solution with vectors

`vec(ER)=1/6vec(EF)`

`vec(EF)= (((11),(4))-((4),(8)))=((7),(-4))`

Therefore,

`vec(ER)=1/6((7),(-4))=((7/6),(-4/6))`

Coordinates of `R` are

`R=((7/6),(-4/6))+((4),(8))=((31/6),(44/6))=((5.17),(7.33))`