Answer:
y = (-1,1)
Step-by-step explanation:
If a point y [tex](x_p,y_p)[/tex] divides a line A [tex](x_1,y_1)[/tex] B [tex](x_2,y_2)[/tex] in the ratio a:b, the formula to find the coordinates of the point y is:
[tex]x_p=x_1+\frac{a}{a+b}(x_2-x_1)[/tex]
and
[tex]y_p=y_1+\frac{a}{a+b}(y_2-y_1)[/tex]
We know Point A is (-3,4) and Point B is (3,-5). And the ratio is a:b or 1:2, so we can say:
[tex]x_1[/tex] = -3
[tex]x_2[/tex] = 3
[tex]y_1[/tex] = 4
[tex]y_2[/tex] = -5
a = 1
b = 2
Plugging these into the formula, we get:
[tex]x_p=-3+\frac{1}{1+2}(3--3)\\x_p=-3+\frac{1}{3}(6)\\x_p=-1[/tex]
and
[tex]y_p=4+\frac{1}{1+2}(-5-4)\\y_p=4+\frac{1}{3}(-9)\\y_p=1[/tex]
So the point y is (-1,1)
