A line is perpendicular to the line 2x - 4y + 7 = 0 and that passes through the point P(7,2). Determine the equation of this line in Cartesian form.
3. The Attempt at a Solution
Okay, so how I generally believe how to solve these problems may be wrong but I'm not sure.
1.The normal vector is (2, -4) so by using this info i found the directional vector to be (4,2)
2. After finding the directional vector, i used the dot product to find a vector that is perpendicular to (4,2) so i got (-2,4). I believe that this vector must be parallel to (2,-4) because otherwise it doesn't make sense(atleast to me)
3. After finding the normal vector to (4,2), i used this information to simulate part of the Cartesian Equation.
4. -2x + 4y = -C; What I did from here was use the specific point i was given (7,2) and implemented it into the x and y values. I got -2(7) + 4(2) = -6
5. My cartesian equation is essentially -2x + 4y -6 = 0.
I'm getting the right answers for some questions but the wrong one for this one, can anyone help out?