question_answer

The extremities of the diagonal of a parallelogram are the points (3, - 4) and (- 6, 5). Third vertex is the point (- 2, 1). Find its fourth vertex.

A)  (1, 1)                           

B)  (1, 0)            

C)  (0, 1)                           

D)  (- 1, 0)

Correct Answer: D

Solution :

(d): Let fourth vertex be (x, y) Considering the coordinates of O, which is the mid-point of diagonals. \[\frac{3-6}{2}=\frac{x-2}{2}\] and \[\frac{-4+5}{2}=\frac{y+1}{2}\] \[\Rightarrow \]\[-3+2=x\] and \[1=y+1\]; \[\Rightarrow \]\[x=-1\] and \[y=0\]