anonymous
  • anonymous
Find the distance from the point (2,-1) to the line y = 2x + 3
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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amistre64
  • amistre64
y = -1/2 x +(2)/2 - 1 y = -1/2 x seems to be the line with the point on it system of equation to find the intersection then distance it from point to point
amistre64
  • amistre64
2x+3 = -1/2 x 5/2 x = -3 x = -3/(5/2) = -6/5 maybe :)
amistre64
  • amistre64
-1/2 * -6/5 = 6/10 = 3/5 then 2(-6/5) + 3 = -12/5 + 15/5 = 3/5 so thats a match

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anonymous
  • anonymous
My correct answer says : 8/5 * sqrt(5), could you help me to get there?
amistre64
  • amistre64
(10/5, -5/5) - (-6/5 , 10/5) --------------- (16/5)^2 + (-15/5)^2 sqrt(16^2+15^2)/5 should be it then
amistre64
  • amistre64
seeing how i thought my first explanation was suffieicnt; youll have to address where it is your following goes amiss at
amistre64
  • amistre64
other than typos :)
amistre64
  • amistre64
|dw:1327864212303:dw|
amistre64
  • amistre64
y = 2x + 3 needs a perp line to it; perp line is just flip and negate the slope 2 flips to -1/2 y = -1/2 x + b ; use (2,-1) to calibrate 2 = -1(-1)/2 + c 2 = 2 + c ; c = 0 y = -1/2 x is equation of line perp to and containing (2,-1)
amistre64
  • amistre64
if we know where the lines meet, we have a point of reference to measure distance with ...|dw:1327864376411:dw|
amistre64
  • amistre64
y = 2x + 3 -( y = -1/2 x) ------------- 0 = 5/2 x + 3 ; when x = -3/5
amistre64
  • amistre64
y = -1/2 * -3/5 = 3/10 therefore, point of intersection is: (-3/2 , 3/10) looks better
amistre64
  • amistre64
(-3/5 , 3/10) that is
amistre64
  • amistre64
|dw:1327864617337:dw|
amistre64
  • amistre64
use distance formula for distance
amistre64
  • amistre64
ugh!!, lost my x ... 5/2 * -2/5 * 3 = -6/5 0 = 5*-6/2*5 + 3 0 = -30/10 + 3 = -3+3 x = -6/5 ....
amistre64
  • amistre64
y = -1/2*-6/5 = 6/10 = 3/5 (-6/5, 3/5) is the point of intersection .....
amistre64
  • amistre64
\[d=\sqrt{(2-\frac{-6}{5})^2+(-1-\frac{3}{5})^2}\] \[d=\sqrt{(\frac{10+6}{5})^2+(\frac{-5-3}{5})^2}\] \[d=\sqrt{(\frac{16}{5})^2+(\frac{-8}{5})^2}\] \[d=\frac{\sqrt{16^2+8^2}}{5}\]
amistre64
  • amistre64
that simplifies to 8sqrt(5)/5
anonymous
  • anonymous
|dw:1327864993315:dw|
anonymous
  • anonymous
that is what we found?
amistre64
  • amistre64
yes
anonymous
  • anonymous
Why doesn't using the pythagorean theorem work here?
amistre64
  • amistre64
it does, but first you need to know 2 points. the given point (2,-1) and the intersection of the perped lines
amistre64
  • amistre64
once you know the 2 points, the distance formula IS the pythag thrm
anonymous
  • anonymous
" the intersection of the perped lines" confused me, I am really stumped because, I still don't understand why we can't just draw the right triangle from the y axis to the point 2,-1
amistre64
  • amistre64
because you dont want the distance from the y axis, you want the distance to the line and the point; that distance is defined as the shortest distance between the line and the point. which just so happens to make a 90degree angle when it hits|dw:1327865470057:dw|
amistre64
  • amistre64
teh y axis has nothing to do with it at all
anonymous
  • anonymous
OH, THE POINT OF PERPENDICULAR(ness)? to the point 2,-1?
amistre64
  • amistre64
yes
anonymous
  • anonymous
which is the part where we found the perp. point? that is the next step correct?
anonymous
  • anonymous
we do the negative inversse, OH, then we go from the point 2,-1 towards the other line, using the perpendicular slope, is that right?
anonymous
  • anonymous
until there is an intersection
amistre64
  • amistre64
yep
anonymous
  • anonymous
is there an equation to find that point?
amistre64
  • amistre64
its solving a system of equations; y = 2x + 3 y = -1/2x we can sub, eliminate, or any other method to solve the sytem
amistre64
  • amistre64
it turns out that i used elimination and came up with those fractions
amistre64
  • amistre64
y = -1/2 x -2y = x, sub in top y = 2(-2y) + 3 y = -4y + 3 5y = 3 y = 3/5
amistre64
  • amistre64
knowing y, solve for x
amistre64
  • amistre64
3/5 = -1/2 x -2*3/5 = x -6/5 = x
amistre64
  • amistre64
those x and y parts are the point of intersection
anonymous
  • anonymous
ahhh, i understand now... now i use the distance formula between the points (-6/5, 3/5) and (2,-1) Hey, i'd like to thank you for spending about an hour of your time to help me understand this, i appreciate it, much kudos to you.
amistre64
  • amistre64
youre welcome :)

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