Answer :

Answer:

Step-by-step explanation:

NP:OP is 1:3          1 + 3  = 4    

  point P is 1/4th of the way from N to O  

N is  -3,-8    and   O is   1, 0

For 'x'   from -3   to 1    is a distance of 4 units   ....  1/4 of this would be '1'

         add this to -3 to get the 'x' coordinate of   -2

For 'y' the distance from -8 to 0 is 8 units.... 1/4 of this is 2 units...add this to -8 to get the 'y' coordinate  of   -6

Point O is then at   -2, -6      Plot that on the line for your answer  

Bqre

Answer:

P(-2, -6)

Step-by-step explanation:

Section Formula

Some two points, A(x1, y1) and B(x2, y2), form segment AB.
Let us assume there exists some point C(x3, y3) such that:

[tex]\frac{\text{AC}}{\text{CB}} = \frac kl[/tex]

Then the following is always true about point C's coordinates:

[tex]x_3 = \frac{l \times x_2 + k \times x_1}{l + k}\\\\y_3 = \frac{l \times y_2 + k \times y_1}{l + k}[/tex]

Analyzing The Problem

The two endpoints are N(-3, -8) and O(1, 0).
The point P(x3, y3) lies on the segment NO such that:

[tex]\frac{\text{NP}}{\text{OP}} = \frac13 = \frac kl[/tex]

Therefore, according to the section formula:

[tex]x_3 = \frac{3 \times -3 + 1 \times 1}{3 + 1} = \frac{-9 + 1}4 = \frac{-8}4 = -2\\\\y_3 = \frac{3 \times -8 + 1 \times 0}{3 + 1} = \frac{-24 + 0}4 = \frac{-24}4 = -6[/tex]

The coordinates of point P are (-2, -6).