We know that the diagonals of a parallelogram bisect each other. Therefore, the coordinates of the mid-point of AC are same as the coordinates of the mid-point of BD.
The coordinates of the mid-point of a line formed by joining two points (x1,y1) and (x2,y2) are (x1+x22,y1+y22)
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Midpoint of AC = (−2+42,−1+b2)
Midpoint of BD = (a+12,0+22)
[1]
⇒ (−2+42,−1+b2) = (a+12,0+22)
⇒ (1,b−12)=(a+12,1)
⇒ a+12 = 1 and b−12 = 1
⇒ a + 1 = 2 and b - 1 = 2
⇒ a = 1 and b = 3
[1]
We know that the diagonals of a parallelogram bisect each other. Therefore, the coordinates of the mid-point of AC are same as the coordinates of the mid-point of BD.
The coordinates of the mid-point of a line formed by joining two points (x1,y1) and (x2,y2) are (x1+x22,y1+y22)
Midpoint of AC = (−2+42,−1+b2)
Midpoint of BD = (a+12,0+22)
⇒ (−2+42,−1+b2) = (a+12,0+22)
[1]
⇒ (1,b−12)=(a+12,1)
⇒ a+12 = 1 and b−12 = 1
⇒ a + 1 = 2 and b - 1 = 2
⇒ a = 1 and b = 3
[1]