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
on AB¯¯¯¯¯¯¯¯
such that the ratio of AP
to PB
is 1:3.

(1 point)
Responses

P(−1,−1)

upper P left parenthesis negative 1 comma negative 1 right parenthesis

P(12,112)

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

P(−245,−235)

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

P(−212,−214)

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 = (-2 1/2, -2 1/4).