Coordinate Geometry Question 140
Question: If $ A(3,5),B(-5,-4),C(7,10) $ are the vertices of a parallelogram, taken in the order, then the co-ordinates of the fourth vertex are
[Kerala (Engg.) 2005]
Options:
A) (10, 19)
B) (15, 10)
C) (19, 10)
D) (19, 15)
E) (e) (15, 19)
Show Answer
Answer:
Correct Answer: E
Solution:
(e) Mid point of $ A(3,5) $ and $ C(7,10) $ = $ M( 5,\frac{15}{2} ) $ Mid point of $ BD=M( 5,\frac{15}{2} ) $
$ B(-5,-4) $ and $ D(x,y) $ $ \frac{-5+x}{2}=5 $ ; $ x=10+5=15 $
$ \frac{-4+y}{2}=\frac{15}{2} $ ; $ y=15+4=19 $ Co-ordinates of fourth vertex $ D=(15,\ 19) $ .
BETA
