Question

Messi kicks a soccer ball from a position that is 3 meters from a sideline and 4 meters from a goal

Answer 1

Answer:

$( 4.8 ,7.6)$

Step-by-step explanation:

We want to find the point, B(x,y) that divides the directed line segment from Messi, M(3,4) to S(6,10) in the ratio m:n=3:2

We use the section formula:

$( \frac{mx_2+nx_1}{m + n} ,\frac{my_2+ny_1}{m + n})$

We substitute the coordinates and the ratio into the section formula to get:

$( \frac{3 \times 6+2 \times 3}{3 + 2} ,\frac{3 \times 10+2 \times 4}{3+ 2})$

We simplify to get:

$( \frac{18+6}{5} ,\frac{30+8}{5})$

This gives us:

$( \frac{24}{5} ,\frac{38}{5})$

$( 4.8 ,7.6)$