The endpoints of segment rs are r(-4, 3) and s(8, -5). complete each statement using a fraction.
a. (-1, 1) is the point of the way from r to s.
b. (5, -3) is the point of the way from r to s.

a. (-1 , 1) is the point at 1 : 3 of the way from R to S

b. (5 , -3) is the point at 3 : 1 of the way from R to S

Step-by-step explanation:

* Lets explain how to solve the problem

- If point (x , y) divide a line segment whose end points are

  and , at ratio

  from the first point, then

  and

* Lets solve the problem

a.

∵ RS is a line segment whose end points are R (-4 , 3) and S (8 , -5)

∵ Point (-1 , 1) divides it at ratio from R

- By using the rule above

∴

- By using cross multiplication

∴ =

- By collecting in one side and in the

 other side

∴

- Divide both sides by 3

∴

∴

∴ (-1 , 1) is the point at 1 : 3 of the way from R to S

b.

∵ RS is a line segment whose end points are R (-4 , 3) and S (8 , -5)

∵ Point (5 , -3) divides it at ratio from R

- By using the rule above

∴

- By using cross multiplication

∴ =

- By collecting in one side and in the

 other side

∴

- Divide both sides by 3

∴

∴

∴ (5 , -3) is the point at 3 : 1 of the way from R to S