Respuesta :
Answer:
B(–1, 4)
Step-by-step explanation:
We want to find a point P(x,y).
Since it is on the directed line segment AB in the ratio 1:3, it means that:
[tex]P - A = \frac{1}{1+3}(B-A)[/tex]
So
[tex]P - A = \frac{1}{4}(B-A)[/tex]
We apply this to both the x-coordinate and y-coordinate of P.
x-coordinate:
x-coordinate of A: -3
x-coordinate of B: 5
x-coordinate of P: x
So
[tex]P - A = \frac{1}{4}(B-A)[/tex]
[tex]x - (-3) = \frac{1}{4}(5 - (-3))[/tex]
[tex]x + 3 = \frac{1}{4} \times 8[/tex]
[tex]x + 3 = 2[/tex]
[tex]x = -1[/tex]
y-coordinate:
y-coordinate of A: 1
y-coordinate of B: 13
y-coordinate of P: y
So
[tex]P - A = \frac{1}{4}(B-A)[/tex]
[tex]y - 1 = \frac{1}{4}(13 - 1)[/tex]
[tex]y - 1 = \frac{1}{4} \times 12[/tex]
[tex]y - 1 = 3[/tex]
[tex]y = 4[/tex]
So the correct answer is given by option B.
