Question

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

Answer 1

given
Q (3, 2) and the mid-points of the sides through Q being (2, -1) and (1, 2).

let P (x,y) and the mid pointt of the side PQ be (2,-1)

applying mid point theroram

So, the vertices of the triangle are P(1,-4), Q(3,2) and R(-1,2).

Now, area of triangle PQR = $\frac{1}{2}|1(2-2)+3(2+4)-1(-4-2)|=12$ sq. units