## Solve Lesson 23 Page 67 SBT Math 10 – Kite>

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.

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 $$\left( {\frac{{1400}}{3};300} \right)$$.