Question

Partition segment MR into a 2:1 ratio with point L. What are the coordinates of L?

M-(-2,-3)
R-(7,9)

Answer 1

The coordinates of L are (4,5)

Explanation:

Partition

Given the points M(-2,-3) R(7,9), we must find a point L(x,y) such that the distance from M to L is double the distance from L to R. This means:

`\overline{ML}=2.\overline{LR}`

We'll apply that relation on both axes separately:

`x_M-x=2(x-x_R)`

`-2-x=2(x-7)`

Operating:

`-2-x=2x-14`

Joining like terms:

`3x=12`

Solving:

`x= 12/3=4`

Now for the y-axis:

`y_M-y=2(y-y_R)`

`-3-y=2(y-9)`

Operating

`-3-y=2y-18`

Joining like terms:

`3y=15`

Solving

`y=15/3=5`

Thus the coordinates of L are (4,5)