Question

Point upper A has coordinates left parenthesis negative 3 comma 1 right parenthesis. Point upper B has coordinates left parenthesis negative 8 comma 5 right parenthesis.

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

=

1
:
2
.

(1 point)
Responses

X(−313,83)
𝑋
(
−
3
1
3
,
8
3
)
X left parenthesis negative 3 1 over 3 comma 8 over 3 right parenthesis

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

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

Answer 1

AX:BX = 1:2 means X is 1/3 of the way from A to B.

B − A = (−8 − (−3), 5 − 1) = (−5, 4)
X = A + (1/3)(B − A) = (−3,1) + (−5/3, 4/3) = (−14/3, 7/3)

So X = (−14/3, 7/3) = (−4 2/3, 2 1/3). This is not one of the given choices.