Question

Question:Use the image to answer the question.Point $A$ has coordinates $(-4, -3)$. Point $B$ has coordinates $(1, 2)$.Find the coordinates of point $X$ if it partitions the directed segment $\overline{AB}$ in the ratio $1:2$.(1 point)Multiple Choice Options (Responses)( ) $X \left(-2\frac{1}{3}, -1\frac{1}{3}\right)$( ) $X \left(-5, -4\frac{2}{3}\right)$( ) $X \left(-1, -\frac{2}{3}\right)$( ) $X \left(-5\frac{1}{4}, -2\frac{1}{2}\right)$

Answer 1

AX:XB = 1:2 so X = A + (1/3)(B − A). B − A = (5,5), (1/3)(5,5) = (5/3,5/3).
X = (−4 + 5/3, −3 + 5/3) = (−7/3, −4/3) = (−2 1/3, −1 1/3).

Answer: first option.