Question

1. determine the distance between twogiven lines
> L1 2x - y = 5
> L2 4x - 2y = 7
2. determine the equation of the line passing through the given point ( -1,-1) and perpendicular to x -y + 3 = 0
3. determine the equation of the line passing through the given point (-2 , 5) and parallel to x + 3y - 5 = 0

FORMULAS:
absolute value of AX BY +C all over 2a (short method)
square root of (X1+X2)(Y1+Y2) (long method)

Answer 1

#2 to be perpendicular, the line passing through (-1, -1) must have the inverse slope of the second line. since the other line (solving for x) is equal to x=y-3, the new line must have equation of the form x=-y+b where b is some variable. pluggin gin the given point (-1 -1) you get -1=1+b, b=-2 so the new equation will be x=-y-2, which in the original form is x+y+2=0

Answer 2

#3 to be parallel, the two lines must have the same slope. the given line translates to x=-3y+5, the new line must be of the form x=-3y+b, plugging in the desired coordinates, -2=-15+b, b=13, so the equation is x=-3y+13, of the original form, this is x+3y-13=0