Question

Find the area of the triangle PQR with Q(3,2) and midpoints of the sides through Q being (2,-1) and (1,2).

Answer 1

HELLO DEAR,


LET THE CO-ORDINATES OF P AND R be (a,b) AND (c,d) 

USING SECTION FORMULA:
(2 , - 1) IS THE MID-POINT OF PQ



$2 = \frac{3 + a}{2 } \\ = > - 1 = \frac{2 + b}{2} \\ = > a = 1 \\ = > b = - 4 \\ = >$
(1 , 2) is the mid-point of QR hence
$1 = \frac{3 + c}{2} \\ c = - 1 \\ = > 2 = \frac{2 + d}{2} \\ = > d = 2$
Therefore, co-ordinates of P and Q are (1 , - 4) and (- 1 , 2)
$area \: of \: triangle \: pqr \\ > \frac{1}{2} \times (3( - 4 - 2) + 2( - 1 - 1) + 1(2 - 4)) \\ = > \frac{1}{2} \times ( - 18 - 4 - 2) \\ = > \frac{1}{2} \times - 24 \\ = > - 12 {unit}^{2}$
Hence area of triangle PQR is 12 sq. units



I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

HOPE THIS ATTACHMENT HELPS YOU ❤️