Find the ares if triangle PQR with Q(3,2) and the mid points of the sides through Q being (2,-1) and (1,2)

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Find the ares if triangle PQR with Q(3,2) and the mid points of the
sides through Q being (2,-1) and (1,2)

Neha Sethi · Accepted Answer

Dear student
Given: the coordinates of Q are 3,2Let the coordinates of P be x1,y1 and R  be  x3,y32,-1 is the mid point of P and QUsing mid point formula, we have2=x1+32  and -1=y1+22⇒x1=1   and y1=-4So, the coordinates of P are 1,-4Let the coordinates of R are x3,y3Now 1,2 is the mid point of Q and RUsing mid point formula, we have1=3+x32  ,2=2+y32x3=-1  and  y3=2So, coordinates of R are -1,2Area of △PQR with x1,y1=1,-4, x2,y2=3,2 and x3,y3=-1,2 =12x1y2-y3+x2y3-y1+x3y1-y2=1212-2+32+4+-1-4-2=120+18+6=12 so, area is 12 sq
 units
Regards