Having trouble understanding concepts (1 Viewer)

[James_]

Hey all,
Can anyone give me advice on how to understand the concepts mathematics touches on? At the moment I need help understanding linear equations you know the stuff like:

d = |ax1+by1+c|
________
sqrt((a)**2+(b)**2)

I hope I am making sense...
I mean I know how to use formulas, its plug and play. But I don't know how to use it for questions that revolve around manipulating the formulas. So any help is appreciated.

 

[Drongoski]

Hey all,
Can anyone give me advice on how to understand the concepts mathematics touches on? At the moment I need help understanding linear equations you know the stuff like:

d = |ax1+by1+c|
________
sqrt((a)**2+(b)**2)

I hope I am making sense...
I mean I know how to use formulas, its plug and play. But I don't know how to use it for questions that revolve around manipulating the formulas. So any help is appreciated.

Suppose u have a line whose eqn is: 3y = 4x - 7

and you are asked to find the perpendicular distance D of point P(-3, 2) from this line.

Then 1st u convert the eqn to the general form, viz: 4x-3y - 7 = 0. Then apply the formula to get:

D = abs{ 4x - 3y - 7}/sqrt(a^2 + b^2)
= abs(4*(-3) -3*(2) - 7}/sqrt(4^2 +(-3)^2)
= abs(-12 -6 -7)/sqrt(25) = 25/5 = 5

Now suppose you use the eqn: 12x - 9y -21 = 0 . This is still the same line as
4x - 3y - 7 = 0. So would u get a different D for this eqn? No.

D = abs{12*(-3) - 9*(2) -21}/sqrt(12^2 + (-9)^2) = 3 * 25/ (3 * 5) = 5

as u should expect. The denominator sqrt(a^2 + b^2) acts to normalise the result. Thus u can multiply the eqn: 4x - 3y -7 by 675, say, and you would still get D = 5.

Hope this makes sense.