Line segment line segment A B has endpoints A negative 4 comma negative 10 and B negative 11 comma negative 7 To find the x -coordinate of the point that divides the directed line segment in a ratio, the formula 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 was used to find that x is equal to open paren the fraction with numerator 3 and denominator 3 plus 4 close paren times open paren negative 11 minus negative 4 close paren plus negative 4 What is the x -coordinate of the point that divides line segment A B into a ratio of 3 to 4 ratio?
Use the given formula with a = 3, b = 4, x₁ = −4, and x₂ = −11. Then x = (3/(3 + 4))(−11 − (−4)) + (−4) = (3/7)(−7) − 4 = −3 − 4 = −7. The x-coordinate is negative 7, choice B.
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