Question

Use the image to answer the question.

Segment upper A upper B is graphed on a coordinate plane. The x-axis ranges from negative 9 to 1 in increments of 1. The y-axis ranges from 0 to 6 in increments of 1.

Find the coordinates of point X
on segment AB¯¯¯¯¯¯¯¯
that partitions the segment into the ratio AX:BX = 1:2
.

(1 point)
Responses

X(−10 1/3,5)
X left parenthesis negative 10 1 over 3 comma 5 right parenthesis

X(−3 1/3,8/3)
X left parenthesis negative 3 1 over 3 comma 8 over 3 right parenthesis

X(−4 1/3,−10)
X left parenthesis negative 4 1 over 3 comma negative 10 right parenthesis

X(−4 2/3,2 1/3)
X left parenthesis negative 4 2 over 3 comma 2 1 over 3 right parenthesis

Answer 1

From the graph A = (−5, 4) and B = (0, 0). With AX:XB = 1:2, X = (2A + B)/3.

X = ((2(−5) + 0)/3, (2(4) + 0)/3) = (−10/3, 8/3) = (−3 1/3, 8/3).

So choose X(−3 1/3, 8/3).