## (Math Quiz 10 – CT) Let M(2; 0), N(2; 2), P(-1; 3) be the midpoints of sides BC, CA, AB of triangle ABC. The coordinates of point B are:

• Question:

Let M(2; 0), N(2; 2), P(-1; 3) be the midpoints of sides BC, CA, AB of triangle ABC. The coordinates of point B are:

Reference explanation:

Triangle ABC has M; N; P is the midpoint of BC respectively; AC ; AB so PN and MN are the medians of the triangle.

Infer: PN // BC and MN // AB.

Then, quadrilateral PNMB is a parallelogram.

Thus, $$\overrightarrow {PB} = \overrightarrow {NM}$$ with $$\overrightarrow {PB} \left( {x + 1;\,\,y – 3} \right);\overrightarrow {NM } \left( {0;\,\, – 2} \right)$$.

$$\Rightarrow \left\{ {\begin{array}{*{20}{c}} {x + 1 = 0}\\ {y – 3 = – 2} \end{array}} \right. \Leftrightarrow \left\{ {\begin{array}{*{20}{c}} {x = – 1}\\ {y = 1} \end{array} \Rightarrow B\left( { – 1;1} \right)} \right.$$