Answer:
We have point P(-3,-6).
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 3:4, it means that:
[tex]P - A = \frac{3}{3+4}(B - A)[/tex]
So
[tex]P - A = \frac{3}{7}(B-A)[/tex]
We apply this to both the x-coordinate and y-coordinate of P.
x-coordinate:
x-coordinate of A: -9
x-coordinate of B: 5
x-coordinate of P: x
So
[tex]P - A = \frac{3}{7}(B-A)[/tex]
[tex]x - (-9) = \frac{3}{7}(5-(-9))[/tex]
[tex]x + 9 = \frac{3}{7} \times 14[/tex]
[tex]x + 9 = 6[/tex]
[tex]x = -3[/tex]
y-coordinate:
y-coordinate of A: -9
y-coordinate of B: -2
y-coordinate of P: y
So
[tex]P - A = \frac{3}{7}(B-A)[/tex]
[tex]y - (-9) = \frac{3}{7}(-2-(-9))[/tex]
[tex]y + 9 = \frac{3}{7} \times 7[/tex]
[tex]y + 9 = 3[/tex]
[tex]y = -6[/tex]
We have point P(-3,-6).
