Find the coordinates of point p along the directed line segment ab so that the ratio of ap to pb is 1 to 4. a(8,0),b(3,−2)

Lines can be divided into smaller segments by using ratios.

The coordinate of P is

The given parameters are:

Line ratio is calculated using

So, we have:

Hence, the coordinate of P is

Read more about line ratios at:

link

(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)

- 70

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