Question

Point E is located at (−2,4) and point F is located at (5,10) . What are the coordinates of the point that partitions the directed line segment EF⎯⎯⎯⎯⎯ in a 7:3 ratio? Enter your answer, as decimals, in the boxes.

Answer 1

Solution:

Coordinates of Point E and F are (-2,4) and (5,10).

Suppose the Point M(x,y), divides the Line Segment Joining E (-2,4) and F (5,10) in the 7:3 ratio.

So, EM: MF= 7:3

Formula for internal Division

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

$x=\frac{3 \times (-2) +7 \times 5}{3 +7},\\\\ x=\frac{-6 +35}{10}\\\\x=\frac{29}{10}\\\\ y =\frac{3 \times 4 +7 \times 10}{3+7}\\\\ y=\frac{12+70}{10}\\\\ y=\frac{82}{10}$

So,we get

x= 2.9

and , y= 8.2