Find the distance between the given point and line in each problem

(3,4) 3x + 5y - 4 =0

Question

Find the distance between the given point and line in each problem

(3,4) 3x + 5y - 4 =0

raffle_snaffle · Answer

use the distance formula

raffle_snaffle · Answer

https://www.google.com/search?q=distance+formula&tbm=isch&tbo=u&source=univ&sa=X&ei=XXbwUo_wGYfyoASikYLQDg&ved=0CDEQsAQ&biw=1366&bih=643#facrc=_&imgdii=_&imgrc=lCL5kVe5vsaFzM%253A%3Bpqop7_Eu8omN4M%3Bhttp%253A%252F%252Fcs.selu.edu%252F~rbyrd%252Fmath%252Fdistance%252Fdist_ex1.gif%3Bhttp%253A%252F%252Fcs.selu.edu%252F~rbyrd%252Fmath%252Fdistance%252F%3B439%3B171

anonymous · Answer

I have the formula, just don't know how to setup.

tkhunny · Answer

Do you have this?  $\dfrac{|3(3) + 5(4) - 4|}{\sqrt{3^{2} + 5^{2}}}$

It is a very important formula.

anonymous · Answer

@tkhunny I wasn't sure how to set it up in the formula, but that helps alot. Thank you!

anonymous · Answer

Would the answer be 5.103? From 25/sqrt 34 ?

mathmale · Answer

An alternative way in which to solve this problem is to determine the equation of the line through the given point (3,4) that is also perpendicular to the given line 3x+5y-4=0.
Then the problem reduces to finding the point of intersection of this perpendicular line with the given line, and, lastly, finding the distance between (3,4) and this intersection.  Not as elegant a solution as tkhunny's, but if you don't have that formula for the distance between a point and a line, this method will succeed.

anonymous · Answer

Thank you! I actually do have the formula. I just needed guidance on setup.

anonymous · Answer

Can you confirm the answer? @mathmale

mathmale · Answer

Please refer to http://mathworld.wolfram.com/Point-LineDistance2-Dimensional.html The distance formula mentioned by tkhunny is about half way down the page. I'd guess that the challenge for you lies in identifying the values of a, b and c. x0 and y0 are the coordinates of the given point. a, b and c are the constant coefficients of the line AFTER it has been written in the form ax+by+c=0; in this case 3x+5y-4 yields a=3, b=5 and c=-4. If you've already recognized this and have evaluated that point-to-line distance formula, your outcome should be correct.