Coordinate Geometry Question 107
Question: The extremities of a diagonal of a parallelogram are the points $ (3,-4) $ and $ (-6,5) $ . If third vertex is $ (-2,1) $ , then fourth vertex is
[RPET 1987]
Options:
A) $ (1,0) $
B) $ (-1,0) $
C) $ (1,1) $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
Let A (3, - 4) and C(- 6, 5) be the ends of diagonal of parallelogram ABCD. Let B (- 2, 1) and D be (x, y).
Then mid-points of diagonals AC and BD coincide. So $ \frac{x-2}{2}=\frac{-6+3}{2} $ and $ \frac{y+1}{2}=\frac{5-4}{2}\Rightarrow x=-1,y=0 $
$ \therefore $ Coordinates of D are (-1, 0).
BETA
