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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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