Question

find the area of a triangle PQR with Q(3,2) and mid- points of the sides through Q being (2,-1) and (1,2)

Answer 1

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Answer 2

Answer:

$Area\: of \: \triangle PQR\\=12\: square \: units$

Step-by-step explanation:

A triangle PQR with Q(3,2) and mid- points of the sides through Q being A(2,-1) and B(1,2)

$Here,\\x_{1}=3,\:y_{1}=2;\\x_{2}=2,\:y_{2}=-1;\\x_{3}=1,\:y_{3}=2;$

$Area\:of \triangle PQR = 4\times \: Area \: of \triangle QAB$

$=4\times \frac{1}{2} |x_{1}(y_{2}-y_{3})+x_{2}(y_{3}-y_{1})+x_{3}(y_{1}-y_{2})|$

$=2|3(-1-2)+1(2-2)+1(2+1)|$

$=2|3\times (-3)+0+3|$

$=2|-9+3|\\=2|-6|\\=2\times 6\\=12$

Therefore,

$Area\: of \: \triangle PQR\\=12\: square \: units$

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