## Solve Lesson 11 Page 62 SBT Math 10 – Kite>

Topic

In the coordinate plane Oxygenfor three noncollinear points USA(twelfth), WOMEN(thirty first), P(− 1 ; 2). Find the coordinates of the point Q such that quadrilateral MNPQ is a trapezoid with MN // PQ and PQ = 2MN.

From the assumption find the coordinates of the point Q satisfy $$\overrightarrow {PQ} = 2\overrightarrow {NM}$$

Detailed explanation

We have: MN // PQ so $$\overrightarrow {MN}$$ and $$\overrightarrow {PQ}$$ have the same direction

Other way, PQ = 2MN $$\Rightarrow \overrightarrow {PQ} = 2\overrightarrow {NM}$$

Call point coordinates Q is $$Q(a;b)$$. We have: $$\overrightarrow {PQ} = (a + 1;b – 2)$$ and $$\overrightarrow {NM} = ( – 2; – 3)$$

$$\Rightarrow \overrightarrow {PQ} = 2\overrightarrow {NM} \Leftrightarrow \left\{ \begin{array}{l}a + 1 = 2.( – 2)\\b – 2 = 2.( – 3)\end{array} \right \Leftrightarrow \left\{ \begin{array}{l}a + 1 = – 4\\b – 2 = – 6\end{array} \right \Leftrightarrow \left \{ \begin{array}{l}a = – 5\\b = – 4\end{array} \right.$$ . So Q(-5 ; -4)