Question
Mathematics Question on Straight lines
Two sides of a rhombus are along the lines, x−y+1=0 and 7x−y−5=0. If its diagonals intersect at (−1,−2), then which one of the following is a vertex of this rhombus?
A
(-3 , -9)
B
(-3 , -8)
C
(31,−38)
D
(−310,−37)
Answer
(31,−38)
Explanation
Solution
Coordinates of A≡(1,2)
∴ Slope of AE=2
⇒ Slope of BD=−21 ⇒
E of BD is x+1y+2=−21
⇒x+2y+5=0
∴ Co-ordinates of D=(31,3−8)
So, the correct option is (C): (31,−38)