SOLUTION: Find the equation of the locus of all points (x,y) that are equidistant from (-3, 4) and (0, -3). Badly need, ASAP. Thankyou!

Algebra ->  Points-lines-and-rays -> SOLUTION: Find the equation of the locus of all points (x,y) that are equidistant from (-3, 4) and (0, -3). Badly need, ASAP. Thankyou!      Log On


   

Question 1192225: Find the equation of the locus of all points (x,y) that are equidistant from (-3, 4) and (0, -3).
Badly need, ASAP. Thankyou!
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Think what the description looks like, or try to draw or sketch it.

Find the line going through the midpoint of your two given points, and with slope being the negative reciprocal of those two given points.

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Steps omitted here but you may continue with y-1%2F2=%283%2F7%29%28x%2B3%2F2%29-------you can use simple algebra to put into another form if you need.

Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.
Find the equation of the locus of all points (x,y) that are equidistant from (-3, 4) and (0, -3).

Solution 

Let (x,y) be the point of the locus.


Then the equation expressing equidistance from the points (-3, 4) and (0, -3) is


    sqrt%28%28x-%28-3%29%29%5E2%2B%28y-4%29%5E2%29 = sqrt%28%28x-0%29%5E2%2B%28y-%28-3%29%29%5E2%29


    %28x%2B3%29%5E2%2B%28y-4%29%5E2 = x%5E2%2B%28y%2B3%29%5E2


    x%5E2%2B6x%2B9+%2B+y%5E2-8y%2B16 = x%5E2+%2B+y%5E2%2B6y%2B9


    6x - 8y + 25 = 6y + 9


    6x - 14y = 9 - 25


    6x - 14y = -16


    3x -  7y =  -8


ANSWER.  We get the equation of the straight line  3x - 7y = -8  in the general form.

Solved.