Question

LM has the endpoints L at –5 and M at 9. To find the point x so that x divides the directed line segment LM in a 2:3 ratio, use the formula x = (x2 – x1) + x1.

x = (9 – (–5)) + (–5)

x =

Answer 1

The given formula is missing the ratio factor. For a point dividing L(x1 = −5) to M(x2 = 9) in ratio 2:3 (LX:XM = 2:3),

x = x1 + (2/(2+3))·(x2 − x1)
= −5 + (2/5)·(9 − (−5))
= −5 + (2/5)·14
= −5 + 28/5
= 3/5 = 0.6.