Line segment AB has endpoints A(1, 2) and B(5, 3). Find the coordinates of the point that divides the line segment directed from A to B in the ratio of 1:3

Correct C ( 2, 2.25)

Step-by-step explanation:

Given points A(1,2) and B(5,3)

The formula by which we calculate the coordinates of a point, let be C, that divides the line segment in the given ratio is.

Xc = (Xa + λ · Xb) / (1 + λ)  and  Yc = (Ya + λ · Yb) / (1 + λ)

Where λ is the coefficient which depends on the direction of the ratio in this case is:

λ = 1 : 3 = 1/3

Xc = (1 + (1/3) · 5) / (1 + (1/3)) = (1 + (5/3))/ (4/3) = (8/3) / (4/3) = 2

Xc = 2

Yc = (2 + (1/3) · 3) / (1 + (1/3)) = (2 + 1)/ (4/3) = 3 / (4/3) = 9/4 = 2.25

Yc = 2.25

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