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प्रश्न
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)
उत्तर
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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