The midpoint of a segment can be found using the formulas for a directed line segment, x is equal to open paren the fraction with numerator A and denominator A plus b close paren times open paren x sub 2 minus x sub 1 close paren plus x sub 1 and y is equal to open paren the fraction with numerator A and denominator A plus b close paren times open paren y sub 2 minus y sub 1 close paren plus y sub 1 When using these formulas to find a midpoint, which is true?
Answer
A
A is equal to 1 and b is equal to 2
B
A is equal to 2 and A plus b is equal to 2
C
A is equal to 1 and A plus b is equal to 2
D
A is equal to 2 and b is equal to 1
Explanation
The directed-segment formula places the point a fraction a/(a+b) of the way from the first endpoint to the second. A midpoint is halfway along the segment, so this fraction must equal 1/2. That happens when a = 1 and a + b = 2, which is choice C.
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