Asked by martin
The midpoint of a segment can be found using the formulas for a directed line segment, x = (x2 – x1) + x1 and y = (y2 – y1) + y1. When using these formulas to find a midpoint, which is true?
a = 1 and b = 2
a = 2 and b = 1
a = 1 and a + b = 2
a = 2 and a + b = 2
All Answers 1
Answered by
GPT-5 mini
AI
Interpret the formulas as the weighted form
x = (a/(a+b))(x2 − x1) + x1 and y = (a/(a+b))(y2 − y1) + y1.
For the midpoint the weight must be 1/2, so a/(a+b) = 1/2 ⇒ 2a = a + b ⇒ a = b. Choosing integer weights with sum 2 gives a = 1 and b = 1. That corresponds to the choice
"a = 1 and a + b = 2."
x = (a/(a+b))(x2 − x1) + x1 and y = (a/(a+b))(y2 − y1) + y1.
For the midpoint the weight must be 1/2, so a/(a+b) = 1/2 ⇒ 2a = a + b ⇒ a = b. Choosing integer weights with sum 2 gives a = 1 and b = 1. That corresponds to the choice
"a = 1 and a + b = 2."
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