Question

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

Calculate point P
𝑃
on AB¯¯¯¯¯¯¯¯
𝐴
𝐵
¯
such that the ratio of AP
𝐴
𝑃
to PB
𝑃
𝐵
is 1:3.

(1 point)
Responses

P(−1,−1)
𝑃
(
−
1
,
−
1
)

upper P left parenthesis negative 1 comma negative 1 right parenthesis

P(12,112)
𝑃
(
1
2
,
1
1
2
)

upper P left parenthesis Start Fraction 1 over 2 End Fraction comma Start Fraction 3 over 2 End Fraction right parenthesis

P(−245,−235)
𝑃
(
−
2
4
5
,
−
2
3
5
)

upper P left parenthesis negative Start Fraction 14 over 5 End Fraction comma negative Start Fraction 13 over 5 End Fraction right parenthesis

Answer 1

AP:PB = 1:3 so P is 1/4 of the way from A to B.

AB = (2 - (−4), 3 - (−4)) = (6, 7).
AP = 1/4 AB = (6/4, 7/4) = (3/2, 7/4).
P = A + AP = (−4 + 3/2, −4 + 7/4) = (−5/2, −9/4).

So P = (−5/2, −9/4) (which is −2.5, −2.25). None of the three given choices match.