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

(1 point)
Responses

X(−413,−10)
X left parenthesis negative 4 1 over 3 comma negative 10 right parenthesis

X(−423,213)
X left parenthesis negative 4 2 over 3 comma 2 1 over 3 right parenthesis

X(−1013,5)
X left parenthesis negative 10 1 over 3 comma 5 right parenthesis

X(−313,83)

Answer 1

From the graph A = (−6, 1) and B = (−2, 5). For AX:BX = 1:2, X = (2A + B)/3.

Compute:
2A + B = 2(−6,1) + (−2,5) = (−12,2) + (−2,5) = (−14,7)
X = (−14/3, 7/3) = (−4 2/3, 2 1/3)

So X(−4 2/3, 2 1/3).