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

Answer:

The coordinates of L are (4,5)

Step-by-step 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)