Find the area of the triangle formed by joining the midpoints of the sides of the triangle whose vertices are A(2, 1), B(4, 3) and C(2, 5).

Question

Philoid · Accepted Answer

By applying section formula we get the coordinates of mid points of AB,BC and AC.

Mid point of AB = P = {(2 + 4)/2,(1 + 3)/2}

P = (3,2)

Mid point of BC = Q = {(4 + 2)/2,(3 + 5)/2}

Q = (3,4)

Mid point of AC = R = {(2 + 2)/2,(1 + 5)/2}

R = (2,3)

For triangle PQR

Area of triangle

= 1/2(x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂))

= 1/2(3(4–3) + 3(3–2) + 2(2–4))

= 1/2(3 + 3–4)

= 1/2(2)

= 1 sq unit