Question

Please help me
This is analytic geometry

Answer 1

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

Explanation:

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

`\overrightarrow{AB} = (3)/(4)\cdot \overrightarrow{AC}`

`B(x,y) -A(x,y) = (3)/(4)\cdot [C(x,y)-A(x,y)]`

`B(x,y) = (3)/(4)\cdot C(x,y) +(1)/(4)\cdot A(x,y)`

`B(x,y) = (3)/(4)\cdot (-6,-2)+(1)/(4)\cdot (6,-6)`

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