Q15 of 47 Page 1

Find the area of the triangle formed by joining the mid-points of the sides of a triangle, whose coordinates of vertices are (0, –1), (2, 1) and (0, 3).

Let the Points be A(0, –1), B(2, 1) and C(0, 3)

Let the midpoint of AB be P, BC be Q and CA be R


P(x, y) =


⇒ P(x, y) =


Q(x, y) =


⇒ Q(x, y) =


R(x, y) =


⇒ R(x, y) =


Area of the triangle between 3 points = × | x1 × (y2 - y3) + x2 × (y3 - y1) + x3 × (y1 – y2) |


Where x1, y1 are the coordinates of P


x2, y2 are the coordinates of Q


x3, y3 are the coordinates of R


⇒ Area of the Given Triangle = × | 1 × (2- 1) + 1 × (1 - 0) + 0× (0 - 2) |


⇒ Area of the Given Triangle = × | 1 + 1 |


Answer: Area of the triangle is 1 sq. Units


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