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What are the coordinates of the point on the directed line segment from (-8, -2) to
(6,2) that partitions the segment into a ratio of 1 to 3?

Sagot :

Answer:

The coordinates of the point are (-4.5,-1).

Step-by-step explanation:

We want to find point T(x,y).

I am going to say that out points are A(-8,-2) and B(6,2)

Since it partitions the segment in a 1:3 ratio, we have that:.

[tex]T - A = \frac{1}{1+3}(B-A)[/tex]

[tex]T - A = \frac{1}{4}(B-A)[/tex]

We apply this to both the x-coordinate and y-coordinate of T.

x-coordinate:

x-coordinate of A: -8

x-coordinate of B: 6

x-coordinate of T: x.

So

[tex]T - A = \frac{1}{4}(B-A)[/tex]

[tex]x - (-8) = \frac{1}{4}(6-(-8))[/tex]

[tex]x + 8 = \frac{14}{4}[/tex]

[tex]x = \frac{14}{4} - 8[/tex]

[tex]x = \frac{14}{4} - \frac{32}{4}[/tex]

[tex]x = -\frac{18}{4}[/tex]

[tex]x = -4.5[/tex]

y-coordinate:

y-coordinate of A: -2

y-coordinate of B: 2

y-coordinate of T: y.

[tex]T - A = \frac{1}{4}(B-A)[/tex]

[tex]y - (-2) = \frac{1}{4}(2-(-2))[/tex]

[tex]y + 2 = 1[/tex]

[tex]y = -1[/tex]

The coordinates of the point are (-4.5,-1).

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