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).

Question

Philoid · Accepted Answer

To find the area of the triangle PQR, we first find the coordinates of points B and C.

A(2,-1) is the midpoint of PQ.

Midpoint of PQ:

x- coordinate = (x₁ + x₂) / 2

⇒ 2 = (3 + x ) / 2

⇒ 4 = 3 + x

⇒ x = 1

y-coordinate = (y₁ + y₂) / 2

⇒ -1 = (2 + y ) / 2

⇒ -2 = 2 + y

⇒ y = -4

Midpoint of QR:

x- coordinate = (x₁ + x₂) / 2

⇒ 1 = (3 + z ) / 2

⇒ 2 = 3 + z

⇒ z=-1

y-coordinate = (y₁ + y₂) / 2

⇒ 2 = (2 + t ) / 2

⇒ 4 = 2 + t

⇒ t = 2

Therefore, P(1,-4) and R(-1,2) and we know Q(3,2) already.
Now, we find the area of ΔABC,