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