Given:
The coordinates are X (0,0), Y (6,3), and Z (1.5, 0.75).
To find:
The ratio where point Z partitioned segment XY.
Solution:
Section formula: If a point divides a line segment is m:n, then
[tex]Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)[/tex]
Let point Z partitioned segment XY in k:1.
Using section formula, we get
[tex]Z=\left(\dfrac{k(6)+1(0)}{k+1},\dfrac{k(3)+1(0)}{k+1}\right)[/tex]
[tex](1.5,0.75)=\left(\dfrac{6k}{k+1},\dfrac{3k}{k+1}\right)[/tex]
On comparing both sides, we get
[tex]\dfrac{6k}{k+1}=1.5[/tex]
[tex]6k=1.5k+1.5[/tex]
[tex]6k-1.5k=1.5[/tex]
[tex]4.5k=1.5[/tex]
Divide both sides by 4.5.
[tex]k=\dfrac{1.5}{4.5}[/tex]
[tex]k=\dfrac{1}{3}[/tex]
So, the required ratio is
[tex]k:1=\dfrac{1}{3}:1[/tex]
[tex]k:1=1:3[/tex]
Therefore, point Z partitioned segment XY in 1:3.
