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Question 353768: Please help me with this!...I do not understand how to get the other answers without using the letters that I am not allowed to use. I get all confused starting with the 4th question.
If you were to compute frequently the distance of a point from a line it would be handy to have a formula into which you plug the coordinates of the point and the equation of the line. At the end of this problem you will obtain such a formula. To help you along you can use WeBWorK to check your intermediate answers.
Let P be the point (p,q) and L the line y = m x + b. It is not necessary, but if you like you may assume that P lies below the line L. All your answers below should be algebraic expressions in terms of m, b, p and q. The slope of L is ____. The slope of a line perpendicular to L is ____. The line through P perpendicular to L can be written as y = s x + c where s is:___ and c is:___ . That line intersects L in the point Q = (u,v), where u is:___ and v is:___. The distance of P and Q is ____. The expression you enter here may be quite messy. However, if it is correct it can be simplified into a very concise and meaningful form. Make sure you check the solution of this problem when the set closes.
Hint: If you are bewildered by all the symbols ask yourself what they mean in the special case of the preceding problem, and compare your calculations for this problem with the numerical calculations you did earlier.
So here are the answers that I have so far.
1. m
2. -1/m
3. -1/m
4. ?
5. ?
6. ?
7. ?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Let P be the point (p,q) and L the line y = m x + b. It is not necessary, but if you like you may assume that P lies below the line L. All your answers below should be algebraic expressions in terms of m, b, p and q. The slope of L is ____.
The slope of a line perpendicular to L is m__.
The line through P perpendicular to L can be written as y = s x + c
where s is:-1/m___ and c is:(mq+p)/m___ .
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That line intersects L in the point Q = (u,v),
where u is: (mq+q-cm)/(m^2+1)___
and v is:[m^2q +mp+c]/[m^2+1)___.
====================
I'll leave the rest to you.
Cheers,
Stan H.
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The distance of P and Q is ____. The expression you enter here may be quite messy. However, if it is correct it can be simplified into a very concise and meaningful form. Make sure you check the solution of this problem when the set closes.
Hint: If you are bewildered by all the symbols ask yourself what they mean in the special case of the preceding problem, and compare your calculations for this problem with the numerical calculations you did earlier.
So here are the answers that I have so far.
1. m
2. -1/m
3. -1/m
4. ?
5. ?
6. ?
7. ?
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