Question

point c(x,y) divides the distance ab with point a(8,12) and point b(16, 18) in a ratio of 3:5, with ac being shorter than bc. what are the co-ordinates of c? (12,15) (14.5, 12.5) (14.5, 12.5) (11,14.25)

Answer 1

The correct option is:   (11, 14.25)

Explanation

Formula:

If a point divides a line segment joining two points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ in a ratio of $m:n$ , then the co ordinate of that point will be:    $(\frac{mx_{2}+nx_{1}}{m+n}, \frac{my_{2}+ny_{1}}{m+n})$

Given that, two endpoints are  $A(8,12)$ and $B(16,18)$.  Point $C(x, y)$ divides the distance $AB$ in a ratio of  $3:5$

That means,  $(x_{1}, y_{1})= (8,12)$ and  $(x_{2}, y_{2})= (16, 18)$

Also,  $m: n= 3:5$

Now according to the above formula......

$x=\frac{mx_{2}+nx_{1}}{m+n} = \frac{3*16+5*8}{3+5}=\frac{48+40}{8}=\frac{88}{8}=11\\ \\ \\ y = \frac{my_{2}+ny_{1}}{m+n}= \frac{3*18+5*12}{3+5}=\frac{54+60}{8}=\frac{114}{8}=14.25$

So, the co-ordinate of point $C$ will be  $(11, 14.25)$