SOLUTION: Find the minimum distance the line 2x - 3y + 6 = 0 is from the origin.

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Question 964026: Find the minimum distance the line 2x - 3y + 6 = 0 is from the origin.
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
-3y%2B6=-2x
-3y=-2x-6
y=%282%2F3%29x%2B2

The line is above the origin where x=0.

Find the line containing the origin and having slope -3%2F2.
y-0=-%283%2F2%29%28x-0%29
y=-3x%2F2.



Find the intersection point of y=-3x%2F2 and y=%282%2F3%29x%2B2.
-3x%2F2=2x%2F3%2B2
-9x=4x%2B12
-9x-4x=12
-13x=12
x=-12%2F13
-
y=-3%2A%28-12%2F13%29%2F2
3%2A%2812%2F13%29%2F2
y=3%2A6%2F13
y=18%2F13
-
Intersection point, x=-12%2F13, y=18%2F13;



Use either Pythagorean Theorem or the Distance formula to find length or distance from (0,0) to (-12/13, 18/13).

sqrt%28%2812%2F13%29%5E2%2B%2818%2F13%29%5E2%29

sqrt%28%28144%2F13%5E2%29%2B%2818%5E2%2F13%5E2%29%29

sqrt%28%28144%2F13%5E2%29%2B%28324%2F13%5E2%29%29

sqrt%28468%2F13%5E2%29

%281%2F13%29sqrt%28468%29

sqrt%28117%2A4%29%2F13

sqrt%2813%2A9%2A4%29%2F13

3%2A2%2Asqrt%2813%29%2F13

highlight%286%2Asqrt%2813%29%2F13%29