Straight Line Question 264

Question: If $ (-4,5) $ is one vertex and $ 7x-y+8=0 $ is one diagonal of a square, then he equation of second diagonal is

Options:

A) $ x+3y=21 $

B) $ 2x-3y=7 $

C) $ x+7y=31 $

D) $ 2x+3y=21 $

Show Answer

Answer:

Correct Answer: C

Solution:

  • [c] One vertex of square is $ (-4,5) $ and equation of one diagonal is $ 7x-y+8=0 $ Diagonal of a square are perpendicular and bisect each other Let the equation of the other diagonal be $ y=mx+c $ where m is the slope of the line and c is the y intercept. Since this line passes through $ (-4,5) $

$ \therefore 5=-4m+c $? (i) Since this line is at right angle to the line $ 7x-y+8=0 $ or $ y=7x+8, $ having slope $ =7 $ ,
$ \therefore 7\times m=-1 $ or $ m=\frac{-1}{7} $ Putting this value of m in equation (i) we get $ C=\frac{31}{7} $ Hence, equation of the other diagonal is $ y=-\frac{1}{7}x+\frac{31}{7} $ or $ x+7y=31. $