Messi kicks a soccer ball from a position that is 3 meters from a sideline and 4 meters from a goal line. the ball lands at a position that is somwhere ... After watching the replay, the ratio between the distance of Messi and the ball is 3/2 meters to the distance between Suarez and the ball.

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destinycampbell destinycampbell · Answer 1 · 2018-09-15T21:00:10+02:00

The actual answer to this problem is (4.8,7.6)

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ashishdwivedilVT ashishdwivedilVT · Answer 2 · 2022-04-13T10:19:35+02:00

Using the internal division formula the coordinates of the ball are (4.8,7.6).

Let us assume the x-axis as the goal line and the y-axis as the sideline

So, coordinates Messi≡(3,4)

Similarly, coordinates Suarez≡(6,10)

Let us suppose the ball is somewhere in between Messi and Suarez

Suppose coordinates of the ball ≡(a,b)

Since the ratio between the distance between Messi and the ball to the distance between Suarez and the ball is 3/2.

This means ball is internally dividing Messi and Suarez in 3:2

So, applying the internal division formula for a straight line.

If a point (a,b) is internally dividing a line segment with coordinates of endpoints as (x₁,y₁) and (x₂,y₂) in the ratio m:n then

[tex]a= \frac{m_{1}x_2+m_2x_1 }{m+n}[/tex]

[tex]a= \frac{m_{1}y_2+m_2y_1 }{m+n}[/tex]

So, [tex]a = \frac{3*6 + 2*3}{3+2}[/tex]

[tex]a=4.8[/tex]

[tex]b= \frac{3*10+2*4}{3+2}[/tex]

[tex]b=7.6[/tex]

So, the coordinates of the ball≡(4.8,7.6)

Therefore, Using the internal division formula the coordinates of the ball are (4.8,7.6).

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