Question

Please help me This is analytic geometry

Answer 1

Answer:

The coordinates of point B are (-3,-3).

Step-by-step explanation:

Let $A(x,y) = (6,-6)$, $C(x,y) = (-6,-2)$ and $\overrightarrow{AB} = \frac{3}{4}\cdot \overrightarrow{AC}$, then we have the following formula by vectorial definition of a line segment:

$\overrightarrow{AB} = \frac{3}{4}\cdot \overrightarrow{AC}$

$B(x,y) -A(x,y) = \frac{3}{4}\cdot [C(x,y)-A(x,y)]$

$B(x,y) = \frac{3}{4}\cdot C(x,y) +\frac{1}{4}\cdot A(x,y)$

$B(x,y) = \frac{3}{4}\cdot (-6,-2)+\frac{1}{4}\cdot (6,-6)$

$B(x,y) = (-3, -3)$