anonymous
  • anonymous
What is the distance from the point (6,0) to the line y=3x+2?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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amistre64
  • amistre64
which distance you want? shortest most likly
amistre64
  • amistre64
the shortest distance is a perpendicular line....
amistre64
  • amistre64
so to find it, we need the line that is perp to this and the point they intersect

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More answers

anonymous
  • anonymous
Possible answers are 4, \[2\sqrt{10} , \sqrt{26} , and\ 3\sqrt{6}\] so I guess which ever equals one of those
amistre64
  • amistre64
the perp has a product of slopes that equals -1 3x = -1 x = -1/3 0 = -1/3(6) +b b = 2 y = (-1/3)x +2
amistre64
  • amistre64
these lines meet at: 3x+2 = (-1/3)x +2 3x + 1/3x = 0 10/3x = 0 x = 0
amistre64
  • amistre64
they appear to meet at the origin...
amistre64
  • amistre64
they meet at (0,2) if anything lol
amistre64
  • amistre64
id go with 4
anonymous
  • anonymous
Per distance formula is \[d= \frac{ \left| ax +by +c \right| }{ \sqrt{a^2 +b^2}}\]
amistre64
  • amistre64
im prolly wrong since i guessed that lol
amistre64
  • amistre64
y = 3x+2 ..... 0 = -6/3 +b 0 = -2 +b b = 2 y = (-1/3)x +2.... that seems to work out
anonymous
  • anonymous
y= 3x+2 get into general form 3x - y + 2 =0 so this means that a=3 , b=-1 and c=2 in our formulas above, and (x,y) are the coordinates of the point ( 6,0) so x=6 , y=0
anonymous
  • anonymous
d= (9 +2 ) / 2 = 4.5 units
anonymous
  • anonymous
wait thats wrong
amistre64
  • amistre64
3x+2 = (-1/3)x +2 3x = -1/3x when x=0 right?
amistre64
  • amistre64
(0,2) (6,0) 36 + 4 = 40 = sqrt(40)
amistre64
  • amistre64
2sqrt(10)
amistre64
  • amistre64
got it ;)
anonymous
  • anonymous
d = \[\frac { \left| 3(6) + 0 + 2 \right|}{\sqrt{10} }\]
amistre64
  • amistre64
now your cooking with gas;)
anonymous
  • anonymous
20/ sqrt (10)
anonymous
  • anonymous
wtf
amistre64
  • amistre64
20sqrt(10) --------- 10
anonymous
  • anonymous
yes I know
amistre64
  • amistre64
2 sqrt(10)
amistre64
  • amistre64
need a calculator? :)
anonymous
  • anonymous
Very puzzling question lol
amistre64
  • amistre64
just had to get the sleep of my ears to see what i was doin
anonymous
  • anonymous
Well thank you

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