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(−212,−214)

upper P left parenthesis negative Start Fraction 5 over 2 End Fraction comma negative Start Fraction 9 over 2 End Fraction 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(−1,−1)

upper P left parenthesis negative 1 comma negative 1 right parenthesis
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Answer 1

Use the section formula. For AP:PB = 1:3, P = ((3x_A + 1x_B)/4, (3y_A + 1y_B)/4).

x = (3(-4) + 2)/4 = (-12 + 2)/4 = -10/4 = -5/2
y = (3(-4) + 3)/4 = (-12 + 3)/4 = -9/4

So P = (-5/2, -9/4).