Question

(-2,-1),(1,0),(4,3) are three successive vertices of a parallelogram find the fourth vertex find the answer ​

Answer 1

Answer:

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

Therefore (1,2) is the fourth vertex.

Answer 2

$\huge \purple \bigstar \red{solution : }$

Let A(-2, -l), B(1, 0). C(4, 3) and D(x, y) be the vertices of a parallelogram ABCD taken in order. Since, the diagonals of a parallelogram bisect each other. Therefore coordinates of the mid-point of AC = Coordinates of the mid-point of BD.

$\sf \green{ \frac{ - 2 + 4}{2} ,\frac{ - 1 + 3}{2} = \frac{1 + x}{2} , \frac{0 + y}{2} }$

(1,1) = ($\frac{1 + x}{2}, \frac{y}{2}$)

x+1 = 2, y=2

Therefore (1,2) is the fourth vertex