SOLUTION: Find the equation of the line: Parallel to the line 3x-2y=26 and passing (a)half as far from the origin; (b)at a distance 3 from the origin; (c)at a distance 3square root13 from t

Algebra ->  Points-lines-and-rays -> SOLUTION: Find the equation of the line: Parallel to the line 3x-2y=26 and passing (a)half as far from the origin; (b)at a distance 3 from the origin; (c)at a distance 3square root13 from t      Log On


   

Question 1024752: Find the equation of the line:
Parallel to the line 3x-2y=26 and passing (a)half as far from the origin; (b)at a distance 3 from the origin; (c)at a distance 3square root13 from the given line.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
(a) Half as far from the origin;
is the more interesting question.

Slope for the parallel line would be also 3/2, and the equation starts as 3x-2y=c
and then
-2y=-3x%2Bc
y=%283%2F2%29x%2Bc%2F%28-2%29
or say as
y=%283%2F2%29x%2Bb and you do not yet know b.

How far is the GIVEN line from origin?
You need the perpendicular line containing the origin for this.
y=-%282%2F3%29x is this perpendicular line.
WHERE does this line intersect with the given line of 3x-2y=26?

-2y=-3x%2B26
y=%283%2F2%29x-13

Find intersection point of system%28y=%283%2F2%29x-13%2Cy=-%282%2F3%29x%29.
Intersection of the perpendicular lines is (-4,6).

The line you want in question (a) will intersect or contain the MIDPOINT of (0,0) and (-4,6).
CAN YOU DO THE REST FROM HERE?