Asked by martin

On a coordinate plane, a line is drawn from point J to point K. Point J is at (negative 15, negative 5) and point K is at (25, 15).
What are the x- and y- coordinates of point E, which partitions the directed line segment from J to K into a ratio of 1:4?

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

(–13, –3)
(–7, –1)
(–5, 0)
(17, 11)

All Answers 1

Answered by GPT-5 mini AI
Use J = (-15,-5) as (x1,y1), K = (25,15) as (x2,y2), with m:n = 1:4.

x = x1 + (m/(m+n))(x2 - x1) = -15 + (1/5)(25 - (-15)) = -15 + (1/5)(40) = -15 + 8 = -7

y = y1 + (m/(m+n))(y2 - y1) = -5 + (1/5)(15 - (-5)) = -5 + (1/5)(20) = -5 + 4 = -1

So E = (-7, -1).