Find the point on the line 6x + y = 10 that is closest to the point (-3, 3).
2007-04-03 11:10:43 · 3 answers · asked by B-Bon 1 in Science & Mathematics ➔ Mathematics
Make line function y1 which is perpendicular to the given line function y = -6x + 10 and passes through (-3,3)
2007-04-03 11:13:56 · answer #1 · answered by v_2tbrow 4 · 1⤊ 0⤋
Find the line perpendicular to the given line thru the point (-3,3). The intersection of the two lines is the answer.
6x + y = 10
The slope m = -6/1 = -6
The slope of the perpendicular line is the negative reciprocal.
m' = -1/m = -1/-6 = 1/6
The point slope equation of the perpendicular line is:
y - 3 = (1/6)(x - (-3)) = (1/6)(x + 3)
6y - 18 = x + 3
x - 6y = -21
The two lines are
6x + y = 10
x - 6y = -21
Add six times the first equation to the second.
37x = 39
x = 39/37
Plug back into the first equation to solve for y.
6x + y = 10
6(39/37) + y = 10
y = 10 - 6(39/37) = (370 - 234)/37 = 136/37
The closest point on the line to (-3, 3) is (39/37, 136/37).
2007-04-03 19:34:41 · answer #2 · answered by Northstar 7 · 0⤊ 0⤋
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2014-07-20 18:56:57 · answer #3 · answered by Anonymous · 0⤊ 0⤋