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KATRIN_1 [288]
3 years ago
14

What are the coordinates of point B on \overline{AC} such that AB = 1/2 BC

Mathematics
1 answer:
marta [7]3 years ago
5 0

Answer:

C. B(x,y) = \left(3,-\frac{16}{3} \right)

Step-by-step explanation:

Let A(x,y) = (6,-7), B(x,y) = (x,y) and C(x,y) = (-3,-2). From statement we know that AB = \frac{1}{2}\cdot BC, which is equivalent to the following linear algebraic formula:

B(x,y) -A(x,y) = \frac{1}{2}\cdot [C(x,y)-B(x,y)] (1)

B(x,y)-A(x,y) = \frac{1}{2}\cdot C(x,y)-\frac{1}{2}\cdot B(x,y)

\frac{3}{2}\cdot B(x,y) = \frac{1}{2}\cdot C(x,y)+A(x,y)

B(x,y) = \frac{1}{3}\cdot C(x,y) +\frac{2}{3}\cdot A(x,y) (2)

Then, the coordinates of point B on AC are:

B(x,y) = \frac{1}{3}\cdot (-3,-2)+\frac{2}{3}\cdot (6,-7)

B(x,y) = \left(-1, -\frac{2}{3}\right)+\left(4, -\frac{14}{3} \right)

B(x,y) = \left(3,-\frac{16}{3} \right)

Which means that correct answer is C.

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