A) \[x+3y=21\]
B) \[2x-3y=7\]
C) \[x+7y=31\]
D) \[2x+3y=21\]
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 \[x+7y=31.\]
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