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

The given options are:

$(A)y-0=\dfrac{2b}{2a-c}(x-c)\\ (B)y=\dfrac{b}{a-c}x-\dfrac{2bc}{2a-c}\\(C)y=\dfrac{2b}{2a-c}x-\dfrac{bc}{2a-2c}\\(D)y=\dfrac{2b}{2a-c}x-\dfrac{2bc}{2a-c}\\(E)y=\dfrac{2b}{a-c}x-\dfrac{2bc}{a-c}$

Answer:

$(D)y = \dfrac{2b}{2a-c}x - \dfrac{2bc}{2a-c}$

Step-by-step explanation:

The diagram is attached for ease of comprehension.

The slope, m of line BD is given as:  $\dfrac{2b}{2a-c}$

The coordinates of B are: (2a,2b)

The coordinates of D are: (c,0)

From the form of the slope, let us take $(x_1,y_1)=(c,0)$.

Substituting m and $(x_1,y_1)$ into the equation of the line: $y - y_1 = m(x - x_1)$

We obtain:

$y - 0= \dfrac{2b}{2a-c}(x - c)$

Simplifying:

$y = \dfrac{2b}{2a-c}x - \dfrac{2bc}{2a-c}$

The correct option is D.

Answer 2

Answer:

C. y = (2b / a - c) x -(2bc / 2a - c)

Step-by-step explanation:

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