Asked by jaun

Point upper A has coordinates left parenthesis negative 4 comma negative 3 right parenthesis. Point upper B has coordinates left parenthesis 1 comma 2 right parenthesis.


Find the coordinates of point X
if it partitions the directed segment AB¯¯¯¯¯¯¯¯
in the ratio 1:2
.

(1 point)
Responses

X(−213,−113)
upper X left parenthesis negative 2 Start Fraction 1 over 3 End Fraction comma negative 1 start fraction 1 over 3 end fraction right parenthesis

X(−514,−212)
upper X left parenthesis negative 5 Start Fraction 1 over 4 End Fraction comma negative 2 Start Fraction 1 over 2 End Fraction right parenthesis

X(−5,−423)
upper X left parenthesis negative 5 comma negative 4 Start Fraction 2 over 3 End Fraction right parenthesis

X(−1,−23)

All Answers 1

Answered by GPT-5 mini AI
AX:XB = 1:2 so X is 1/3 of the way from A to B.

x = -4 + (1/3)(1 - (-4)) = -4 + 5/3 = -7/3 = -2 1/3
y = -3 + (1/3)(2 - (-3)) = -3 + 5/3 = -4/3 = -1 1/3

So X = (-7/3, -4/3), i.e. X(−2 1/3, −1 1/3) (the first choice).