Answer:
Step-by-step explanation:
We are given a ratio for this problem so we will use the formula for when we are given a ratio (as opposed to the formula for when you are given that the point you're looking for is a fraction of the way from one point to another, like 1/3 of the way from point A to point B. That's a different formula).
The formulas are for the x and y coordinates of the point in question:
[tex]x=\frac{bx_1+ax_2}{a+b}[/tex] and [tex]y=\frac{by_1+ay_2}{a+b}[/tex] where
a = 3 (from the ratio),
b = 1 (from the ratio),
x1 = -4, y1 = 0 (from point J)
x2 = 0, y2 = 4 (from point K). Filling in for x first:
[tex]x=\frac{1(-4)+3(0)}{3+1}[/tex] gives us
[tex]x=\frac{-4}{4}=-1[/tex] and now for y:
[tex]y=\frac{1(0)+3(4)}{3+1}[/tex] gives us
[tex]y=\frac{12}{4}=3[/tex]
Therefore, the coordinates that partition that segment into the ratio of 3:1 are (-1, 3)
