Question

Three vertices of the parallelogram taken in order are ( -1,0),( 3,1 )and (2,2) respectively. Find the coordinate of the fourth vertex.

Answer 1

let the fourth vertex be (x,y)

(note: if we use equal side property of parallelogram to find the equations, we will fall in trouble due to quadratic terms. so we will use different property of parallelogram)

The diagonals of a parallelogram bisect deach other

thus mid point of one diagonal is mid point of other diagonal also

now, mid point of diagonal with vertex (x,y) and (3,1)

= (x+3)/2, (y+1)/2

mid point of diagonals with vertex (-1,0) and (2,2)

= (-1 + 2)/2, (0+2)/2

= 1/2, 1

both mid points are same so,

(x+3)/2 = 1/2

x + 3 = 1

x = -2

(y+1)/2 = 1

y + 1 = 2

y = 1

thus, coordinates are (-2, 1)