Question

Having trouble with how to do this problem
Find the point on the line -4 x + 5 y - 4 =0 which is closest to the point ( -1, -3 )

Answer 1

a point is always closest to a line when at a 90 degree angle
find a line perpendicular to given line that goes through point (-1,-3)

then solve for the point where 2 lines intersect

Answer 2

first get line in slope-intercept form
\[y = \frac{4}{5} x + \frac{4}{5}\]
slope = 4/5
perpendicular slope = -5/4
find equation of line through point (-1,-3) using point slope form
\[y-(-3) = -\frac{5}{4}(x -(-1))\]
\[y = -\frac{5}{4}x -\frac{17}{4}\]
set lines equal
\[\frac{4}{5}x + \frac{4}{5} = -\frac{5}{4}x - \frac{17}{4}\]
solve for x
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Answer 3

awesome thanks!!!!

Answer 4

yw