Question

The endpoints of the
directed line segment AB
are A (1,7) and B(5, 15).
Find the coordinates of point
P along AB so that the ratio
of AP to PB is 3 to 1.

Answer 1

The coordinates of point P along AB so that the ratio of AP to PB is 3 to 1 is (4,13).

What are coordinates?

A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.

Given that the ratio of the two lines is 3:1, therefore, we can write,

m:n = 3:1

Also, the coordinate of the endpoints of the line are,

A = (x₁, y₁) = (1, 7)

B = (x₂, y₂) = (5, 15)

Now, Using the Section formula the coordinate of the point P can be written as,

$P = (\dfrac{mx_2+nx_1}{m+n}\ , \dfrac{my_2+yx_1}{m+n})\\\\P = (\dfrac{3(5)+1(1)}{4}\ , \dfrac{3(15)+1(7)}{4})\\\\P = (4, 13)$

Hence, the coordinates of point P along AB so that the ratio of AP to PB is 3 to 1 is (4,13).

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