if the points A(1 -2), B(2 3),C(-3 2) and D(-4, -3) form a parallelogram ABCD find its area and heights taking AB as base pls ans this ans because it is important
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given: A(1,-2) , B(2,3) , C(-3, 2) and D(-4, -3)
to find the area of this parallelogram and its height with AB as base
Area of || gram = 2 × area of one of the triangles inside it.
let's find area of ∆ ABC of || gram ABCD
x1 = 1 , x2 = 2, x3 = -3, y1 = -2, y2 = 3 , y3 = 2
=> A = 1/2 [ x1(y2 - y3) + x2(y3 - y1)+x3(y1 - y3)]
=> 1/2 [ 1(3 - 2) + 2(2 - (-2) + (-3)(-2 - 2) ]
=> 1/2 [ 1 + 8 + 12]
=> 1/2 * 21
=> 10.5 cm²
therefore area of parallelogram = 2*10.5 = 21 cm²
now, area of parallelogram A = base × height
AB = √[(x2-x1)² + (y2-y1)²]
AB = √ (2-1)² + {(3 -(-3)}²]
AB = √ (1 + 25)
AB = √26
therefore A = AB×h [ area of || gm = base × height]
21 = √26 × h
=> h = 21/√26 cm
or 21/√26 * √26/√26
=> (21√26)/26
=> 4.12 cm
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