Question

Three consecutive vertices of a parallelo-
gram are (-2, 1), (1, 0) and (4, 3). The
fourth vertex is​

Answer 1

$\underline{\underline{\purple{Given:-}}}$

• Three consecutive vertices of a parallelogram are (-2, 1), (1, 0) and (4, 3).

$\underline{\underline{\red{To \: Find:-}}}$

• The fourth vertex .

$\underline{\underline{\pink{SOLUTION:-}}}$

↝Let A(-2, -l), B(1, 0). C(4, 3) and D(x, y) be the vertices of a parallelogram ABCD taken in order.

• The diagonals of a parallelogram bisect each other.

↝Therefore coordinates of the mid-point of AC = Coordinates of the mid-point of BD.

$➝(-2+4/2, -1+3/2) = (1+x/2, 0+y/2)$$\\➝(1,1) = (1+x/2 , y/2)\\ \\ \\➝x+1 = 2, y=2$

$\sf{\therefore{\underline{\orange{(1,2) \: is \: the \: fourth \: vertex.}}}}$

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Answer 2

$\underline{\underline{\purple{Given:-}}}$

Three consecutive vertices of a parallelogram are (-2, 1), (1, 0) and (4, 3).

$\underline{\underline{\red{To \: Find:-}}}$

The fourth vertex .

$\underline{\underline{\pink{SOLUTION:-}}}$

↝Let A(-2, -l), B(1, 0). C(4, 3) and D(x, y) be the vertices of a parallelogram ABCD taken in order.

• The diagonals of a parallelogram bisect each other.

↝Therefore coordinates of the mid-point of AC = Coordinates of the mid-point of BD.

$➝(-2+4/2, -1+3/2) = (1+x/2, 0+y/2)$$\\➝(1,1) = (1+x/2 , y/2)\\ \\ \\➝x+1 = 2, y=2$

$\sf{\therefore{\underline{\orange{(1,2) \: is \: the \: fourth \: vertex.}}}}$

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