Question

The slope of line Line B D is StartFraction 2 b Over 2 a minus c EndFraction.

Triangle A B C with centroid G is shown on an x and y-axis. Lines are drawn from each point through the centroid to the midpoint of the opposite side to form line segments A F, B D, and C E. Point A is at (0, 0), point D is at (c, 0), point C is at (2 c, 0), point B is at (2 a, 2 b), and point E is at (a, b).

What is the equation of Line B D, simplified?

y − y1 = m(x − x1)
y − 0 = (StartFraction 2 b Over 2 a minus c EndFraction)(x − c)
y = (StartFraction b Over a minus c EndFraction)x − (StartFraction 2 b c Over 2 a minus c EndFraction)
y = (StartFraction 2 b Over 2 a minus c EndFraction)x − (StartFraction b c Over 2 a minus 2 c EndFraction)
y = (StartFraction 2 b Over 2 a minus c EndFraction)x − (StartFraction 2 b c Over 2 a minus c EndFraction)
y = (StartFraction 2 b Over a minus c EndFraction)x − (StartFraction 2 b c Over a minus c EndFraction)

Answer 1

Use point-slope with D(c,0) and m = 2b/(2a−c):

y − 0 = (2b/(2a − c))(x − c)

so

y = (2b/(2a − c))x − (2bc/(2a − c)).