Question

Find the area of  ΔABC with A(1, -4) and midpoints of sides through A being (2, -1) and (0, -1).

Answer 1

Let ( x₂, y₂) and (x₃, y₃) be the coordinates of B and C respectively. Since, the coordinates of A are (1,-4) , therefore

`(1+x_2)/2= 2⇒x_2 = 3`

`(-4+y_2)/2=-1⇒y_2 = 2`

`(1+x_2)/2 =0⇒x_3=-1`

`(-4+y_3)/2 = -1 ⇒ y_3 = 2`

` " let " A (x_1,y_1) = A (1,-4) , B (x_2,y_2) = B(3,2) and C(x_3,y_3) = C (-1,2) Now`

`"Area " (Δ ABC) = 1/2 [x_1(y_2-y_3) +x_2 (y_3-y_1)+x_3(y_1-y
_2)]`

`=1/2 [1(2-2)+(2+4)-1(-4-2)]`

`=1/2[0+18+6]`

=12 sq. units 

Hence, the area of the triangle  ΔABCis 12 sq. units