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 5 to 3 in increments of 1. The y-axis ranges from negative 5 to 4 in increments of 1.

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(−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

P(12,112)

A(-4,-4) B(2,3)

Answer 1

P = A + (1/4)(B − A) because AP:PB = 1:3.

x = −4 + (1/4)(2 − (−4)) = −4 + 6/4 = −5/2
y = −4 + (1/4)(3 − (−4)) = −4 + 7/4 = −9/4

So P = (−5/2, −9/4) = (−2 1/2, −2 1/4).