Question

X divides into the line PQ in the ratio 2:3 P is (2,1) and Q is (12.5,7.5) work out the coordinates of point X

Answer 1

Answer: (6.2, 3.6)

Step-by-step explanation:

We know that  if a point M (x,y) divide a line segment having endpoints $(x_1,y_1)$ and  $(x_2,y_2)$ in ratio m:n , then the coordiantes of M is given by :-

$x=\dfrac{mx_2+nx_1}{m+n}\ ;\ y=\dfrac{my_2+ny_1}{m+n}$

Given : X divides into the line PQ in the ratio 2:3 P is (2,1) and Q is (12.5,7.5).

Then, coordinate of X is given by :-

$x=\dfrac{2(12.5)+3(2)}{2+3}\ ;\ y=\dfrac{2(7.5)+3(1)}{2+3}\\\\\Rightarrow\ x=\dfrac{31}{5}\ ;\ y=\dfrac{18}{5}\\\\\Rightarrow\ x=6.2\ ;\ y=3.6$

Hence, the coordinate of X = (6.2, 3.6)

Answer 2

According to ratio theorem;
x = 2/5(Q) + 3/5(P)
   = 2/5(12.5,7.5) + 3/5(2,1)
   = 2( 2.5, 1.5) + 3( 0.4, 0.2)
   = (5,3) + (1.2,0.6)
   = (6.2, 3.6)
The Coordinates of X will be;
  =(6.2, 3.6)