Locate the point on the line segment A (3,-5) and B (13,-15) given that the point is 4/5 of the way from A to B. Show your work

The coordinates of the point on the line segment between A (3 , -5) and B (13 , -15) given that the point is 4/5 of the way from A to B would be:  (11 , -13)

Step-by-step explanation:

As the line segment has the points:

Let (x, y) be the point located on the line segment which is 4/5 of the way from A to B.

Using the formula

Here, the point (x , y) divides the line segment having end points (x₁, y₁) and (x₂, y₂) in the ratio m₁ : m₂ from the point (x₁, y₁).

As (x, y) be the point located on the line segment which is 4/5 of the way from A to B, meaning the distance from to is units, and  the

distance from to B is 1 unit, as .

Thus

m : n = 4 : 1

so

Finding x-coordinate:

        ∵

Finding y-coordinate:

             ∵

so

Therefore, the coordinates of the point on the line segment between A (3 , -5) and B (13 , -15) given that the point is 4/5 of the way from A to B would be:  (11 , -13)