Answer:
(7, -0.4)
Step-by-step explanation:
Let's start by plotting the two given points A = (8,0) and B = (3,-2) (see attached image). A is shown in orange and B in green.
Notice that A and B are separated from each other 5 divisions horizontally, and 2 divisions vertically. We depicted in red the segment joining both.
In order to divide the segment AB in two pieces such that their ratio AP/PB = 1/4, we need to divide it in exactly 4 + 1 = 5 equal parts, this way, once we locate point P, its distance from point A will be 1/4 of its distance from point B.
Point P has been approximately located in such position in the image.
Now, to calculate the exact position of point P and give it as an order pair, we need to find its x and y locations on the plane.
Since there are exactly 5 horizontal divisions between A and B, the horizontal position of point P will be one division to the left of A, that is: at x=7.
Now for point P vertical position, we consider that there are just 2 vertical division between A and B, and we need 5 subdivisions. therefore, 2 divided by 5 will give us the length of the vertical "steps" we need to consider: 2/5 = 0.4 Therefore, point P should be located at the coordinate pair: (7, -0.4)
