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**Topic**

On the radar screen of the air traffic control tower (referred to as the coordinate plane *Oxygen* with units on axes in kilometers), a helicopter moving in a straight line from the city *A* have coordinates

(600 ; 200) to the city *REMOVE* have coordinates (200 ; 500) and flight time distance *AB* is 3 hours. Find the coordinates of the helicopter at 1 hour after departure.

**Solution method – See details**

Call *OLD* is the place where the plane arrives 1 hour after departure. Find the coordinates of the point *OLD*

Step 1: Calculate coordinates \(\overrightarrow {AB} \)

Step 2: From the hypothesis find the point *OLD* satisfy \(\overrightarrow {AC} = \frac{1}{3}\overrightarrow {AB} \) then conclude

**Detailed explanation**

Call *OLD*(*a*; *b*) is the place where the plane arrives 1 hour after departure

We have: \(\overrightarrow {AB} = ( – 400;300)\)

According to the assumption, *AC *= \(\frac{1}{3}AB\) \( \Rightarrow \overrightarrow {AC} = \frac{1}{3}\overrightarrow {AB} \Leftrightarrow \left\{ \begin{array}{l }a – 600 = \frac{1}{3}.( – 400)\\b – 200 = \frac{1}{3}.300\end{array} \right.\) \( \Leftrightarrow \left \{ \begin{array}{l}a = \frac{{1400}}{3}\\b = 300\end{array} \right \Rightarrow C\left( {\frac{{1400}}{ 3};300} \right)\)

So the coordinates of the helicopter at 1 hour after departure are \(\left( {\frac{{1400}}{3};300} \right)\).

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