Question

If three consecutive vertices of a parallelogram are (1, –2), (3, 6) and (5, 10), find its fourth vertex.

(a) (2, –3) 

(b) (–2, –3) 

(c) (3, 2) 

(d) (3, –2)

Answer 1

(c) (3,2)

Let the vertices of the parallelogram be A (1, –2), B (3, 6), C (5, 10) and D (x, y) since diagonals of a parallelogram bisect each other, mid-point of AC = mid-point of BD

⇒ \(\bigg(\frac{5+1}{2},\frac{10-2}{2}\bigg)\) = \(\bigg(\frac{x+3}{2},\frac{y+6}{2}\bigg)\)

⇒ (3,4) = \(\bigg(\frac{x+3}{2},\frac{y+6}{2}\bigg)\)

Now find x and y.