SOLUTION: Can you help me with this assignment in analytic geometry: Find the distance of the point (12,7) from the line through (5,3) and (2,-3) I need a complete solution. Thank you!

Algebra ->  Proofs -> SOLUTION: Can you help me with this assignment in analytic geometry: Find the distance of the point (12,7) from the line through (5,3) and (2,-3) I need a complete solution. Thank you!      Log On


   

Question 1079374: Can you help me with this assignment in analytic geometry:
Find the distance of the point (12,7) from the line through (5,3) and (2,-3)
I need a complete solution. Thank you!
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.
The line passing through the two given points has the equation

%28y-%28-3%29%29%2F%28x-2%29 = %28-3-3%29%2F%282-5%29,   or

%28y%2B3%29%2F%28x-2%29 = %28-6%29%2F%28-3%29,   or

%28y%2B3%29%2F%28x-2%29 = 2,   which is the same as

y+3 = 2*(x-2),   or

2x - y -7 = 0.

Having this equation, you can check, that your points lie in this straight line.


   (From your course of analytic geometry you must know the procedure I applied above . . . )


On what to do next, see the lesson
    - The distance from a point to a straight line in a coordinate plane
in this site.


You will find there everything you need to complete the solution on your own.



       OK. The last step is this formula for the distance, taken from that lesson:

             d = abs%282%2A12+%2B+%28-1%29%2A7+-+7%29%2Fsqrt%282%5E2+%2B+%28-1%29%5E2%29 = 10%2Fsqrt%285%29 = 2%2Asqrt%285%29.


Also,  you have this free of charge online textbook on Geometry
    GEOMETRY - YOUR ONLINE TEXTBOOK
in this site.

The referred lesson is the part if this textbook under the topic
"The distance from a point to a straight line in a coordinate plane".


Please let me know whether this lesson was useful to you.
Thank you.