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Question
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)
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Solution
The verticals of the triangle are A(2,1) , B (4,3) and C(2,5).
`"Coordinates of midpoint of" AB = P (x_1,y_1)= ((2+4)/2,(1+3)/2) = (3,2)`
`"Coordinates of midpoint of " BC = Q(x_2,y_2) = ((4+2)/2,(3+5)/2) = (3,4)`
`"Coordinates of midpoint of" AC =R (x_3,y_3) = ((2+2)/2, (1+5)/2) = (2,3)`
Now,
`"Area of " ΔPQR =1/2 [x_2(y_2-y_3) +x_2 (y_3-y_1) +x_3 (y_1-y_2)]`
`=1/2[3(4-3)+3(3-2)+2(2-4)]`
`=1/2[3+3-4]=1` sq. unit
Hence, the area of the quadrilateral triangle is 1 sq. unit.
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