Question

The x-coordinate of the intersection point of Line B D and Line C E is StartFraction 2 (a + c) Over 3 EndFraction.

y = (StartFraction b Over a minus c EndFraction)x − (StartFraction 2 b c Over a minus 2 c EndFraction)
y = (StartFraction b Over a minus 2 c EndFraction) (StartFraction 2 (a + c) Over 3 EndFraction) minus (StartFraction 2 b c Over a minus 2 c EndFraction)
y = (StartFraction b Over a minus 2 c EndFraction) (StartFraction 2 (a + c) Over 3 EndFraction) minus (StartFraction 6 b c Over 3(a minus 2 c) EndFraction)
y = StartFraction 2 b (a + c) minus 6 b c Over 3 (a minus 2 c) EndFraction
y = StartFraction 2 a b + 2 b c minus 6 b c Over 3 (a minus 2 c) EndFraction
What is the y-coordinate?

StartFraction b c Over 3 EndFraction
StartFraction 2 b Over 3 EndFraction
StartFraction 2 b c Over 3 EndFraction
StartFraction a b c Over 3 EndFraction

Answer 1

Plug x = 2(a + c)/3 into
y = (b/(a − 2c)) x − (2bc/(a − 2c)):

y = (b/(a − 2c))·(2(a + c)/3) − 2bc/(a − 2c)
= [2b(a + c) − 6bc] / [3(a − 2c)]
= [2ab + 2bc − 6bc] / [3(a − 2c)]
= [2ab − 4bc] / [3(a − 2c)]
= 2b(a − 2c) / [3(a − 2c)]
= 2b/3.

Answer: 2b/3.