Question

Given the coordinates X (0,0), Y (6,3), and Z (1.5, 0.75). Find the ratio where point Z partitioned segment XY.

Show work please

Answer 1

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

`Point=\left((mx_2+nx_1)/(m+n),(my_2+ny_1)/(m+n)\right)`

Let point Z partitioned segment XY in k:1.

Using section formula, we get

`Z=\left((k(6)+1(0))/(k+1),(k(3)+1(0))/(k+1)\right)`

`(1.5,0.75)=\left((6k)/(k+1),(3k)/(k+1)\right)`

On comparing both sides, we get

`(6k)/(k+1)=1.5`

`6k=1.5k+1.5`

`6k-1.5k=1.5`

`4.5k=1.5`

Divide both sides by 4.5.

`k=(1.5)/(4.5)`

`k=(1)/(3)`

So, the required ratio is

`k:1=(1)/(3):1`

`k:1=1:3`

Therefore, point Z partitioned segment XY in 1:3.