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)

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=(mx_2+nx_1)/(m+n)\ ;\ y=(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=(2(12.5)+3(2))/(2+3)\ ;\ y=(2(7.5)+3(1))/(2+3)\\\\\Rightarrow\ x=(31)/(5)\ ;\ y=(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)