Three vertices of a parallelogram are A(2,4), B(6,2) and C(8,6). Find the area of the parallelogram

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justaguide | College Teacher | (Level 2) Distinguished Educator

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Three of the vertices of a parallelogram are A(2,4), B(6,2) and C(8,6).

The area of a parallelogram is given by b*h where b is the length of the base or one of the sides and h is the height or the perpendicular distance of a vertex lying on the opposite side.

Take the vertices A(2, 4) and B(6, 2). The length of AB is `b = sqrt((6 - 2)^2 + (4 - 2)^2) = sqrt(16 + 4) = sqrt 20` . The equation of AB is `(y - 2)/(x - 6) = (4 - 2)/(2 - 6)`

=> `-2*(y - 2) = (x - 6)`

=> `x + 2y -10 = 0`

The perpendicular distance of C from AB is `h = |8 + 12 - 10|/sqrt(1 + 4) = 10/sqrt 5`

The area of the parallelogram is `(10*sqrt 20)/sqrt 5` = 20

The area of the parallelogram with three vertices A(2,4), B(6,2) and C(8,6) is 20