Posted by **Anonymous** on Thursday, October 27, 2011 at 7:19pm.

Find the point on the line -3 x + y - 4 =0 which is closest to the point ( -5, 0 ).

- Calculus -
**Damon**, Thursday, October 27, 2011 at 8:14pm
find slope of original line

y = 3 x + 4

so slope = m = 3

so slope of line perpendicular to original = m' = -1/m = -1/3

so find line through (-5,0) with slope m' of -1/3

y = -x/3 + b

0 = 5/3 + b

b = -5/3

so y = -x/3 -5/3

3y= -x - 5 or x + 3y + 5 = 0

find intersection of lines

-9x + 3y -12 = 0

+1x + 3y + 5 = 0

------------------

8 x -17 = 0

x = 17/8

find y

then find the difference in distance between the two points

d^2 = change in x^2 + change in y^2

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