Question

On a coordinate plane, a line is drawn from point A to point B. Point A is at (7, negative 2) and point B is at (negative 8, negative 9).
What are the x- and y-coordinates of point C, which partitions the directed line segment from A to B into the ratio 5:8? Round to the nearest tenth, if necessary.

x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1

y = (StartFraction m Over m + n EndFraction) (y 2 minus y 1) + y 1

(–2.2, –6.3)
(–2.4, –6.4)
(2.7, –0.7)
(1.2, –4.7)

Answer 1

Use A = (7, −2), B = (−8, −9), m:n = 5:8.

x = 7 + (5/13)(−8 − 7) = 7 + (5/13)(−15) = 7 − 75/13 = 16/13 ≈ 1.2
y = −2 + (5/13)(−9 − (−2)) = −2 + (5/13)(−7) = −2 − 35/13 = −61/13 ≈ −4.7

So C = (1.2, −4.7).