Question

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

Answer 1

The fourth vertex is (1,2)

Let A be (-2,-1), B be (1,0), C be (4,3) and D be (x,y)

The x-coordinate of the mid point of AC is = (-2+4)/2 = 1

Also the x-coordinate of the mid point of BD = (1+x)/2

Since the value of the x-coordinates are equal, so

(1+x)/2 = 1

⇒ 1+x = 2

⇒ x = 2-1 = 1

The y-coordinate of the mid point of AC is = (-1+3)/2 = 1

Also the y-coordinate of the mid point of BD = (0+y)/2

Since the value of the y-coordinates are equal, so

(0+y)/2 = 1

⇒ y = 2

So, the point is (1,2)