Question

The midpoint of a segment can be found using the formulas for a directed line segment, (x = (fraca+b/2)(x₂ - x₁) + x₁); and (y = (fraca+b/2)(y₂ - y₁) + y₁). When using these formulas to find a midpoint, which is true?

a) (a = 1) and (b = 2)
b) (a = 2) and (b = 1)
c) (a = 1) and (a + b = 2)
d) (a = 2) and (a + b = 2)

Answer 1

c) (a = 1) and (a + b = 2). The correct answer is option c) (a = 1) and (a + b = 2).

Step-by-step explanation:

The correct answer to the question is option c) (a = 1) and (a + b = 2).

In the given formulas for finding the midpoint of a segment, (x = (fraca+b/2)(x₂ - x₁) + x₁) and (y = (fraca+b/2)(y₂ - y₁) + y₁), 'a' represents the ratio of the first segment and 'b' represents the ratio of the second segment.

In option c), 'a' is given as 1 and 'a + b' is given as 2, which satisfies the formulas for finding the midpoint.