Maths-
General
Easy

Question

The equations of the sides of the Square for which (3, 4), (1, –1) are the end points of a diagonal are

  1. 7x+3y-33=0,3x-7y+19=0,3x-7y-10=0,7x+3y-4=0    
  2. 6x+2y-31=0,2x-5y+18=0,2x-5y-5=0,2x+5y+1=0    
  3. x+y+5=0,x-y+2=0,5x+3y-11=0,5x+y-1=0    
  4. none of these

hintHint:

find out the slope of the diagonal and find the slopes of the sides . then use the end points of the diagonal to calculate the  equation of the sides.

The correct answer is: 7x+3y-33=0,3x-7y+19=0,3x-7y-10=0,7x+3y-4=0


    3x-7y-19=0, 7x+3y-33=0 , 7x+3y-4=0, 3x – 7y -10=0


    slope of the diagonal : (4-(-1))/ (3-1)
    = 5/2
    Angle made by the sides with the diagonals = 45 degree
    Slope of the sides :
    Tan 45 = |m-(5/2)|/|1+(5m/2)|
    On solving we get
    5m+2=±(2m-5)
    m=-7/3 or 3/7
    equation of sides :
    y-y1=m(x-x1)
    7x+3y-4=0
    3x – 7y -10=0
    Similarly, at (1,-1),
    3x-7y-19=0
    7x+3y-33=0

    tan (x) = (m1-m2)/(1+m1m2). this gives the relationship between the slope and angle between the two line.

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