Question

What are the coordinates of the point on the directed line segment from (-1, -2)(−1,−2) to (9, -10)(9,−10) that partitions the segment into a ratio of 3 to 1?

Answer 1

Answer:

Correct answer:  C (6.5 , - 8)

Step-by-step explanation:

Given points A(-1,-2) and B(9, -10)

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 = 3 : 1 = 3

Xc = (-1 + 3 · 9) / (1 + 3) = (-1 + 27)/ 4 = 26 / 4 = 6.5

Xc = 6.5

Yc = (-2 + 3 · (-10) / (1 + 3) = (-2 - 30)/ 4 = -32 / 4 = - 8

Yc = - 8

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