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anonymous
 4 years ago
Find the distance from the point (2,1) to the line y = 2x + 3
anonymous
 4 years ago
Find the distance from the point (2,1) to the line y = 2x + 3

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amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1y = 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
 4 years ago
Best ResponseYou've already chosen the best response.12x+3 = 1/2 x 5/2 x = 3 x = 3/(5/2) = 6/5 maybe :)

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.11/2 * 6/5 = 6/10 = 3/5 then 2(6/5) + 3 = 12/5 + 15/5 = 3/5 so thats a match

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0My correct answer says : 8/5 * sqrt(5), could you help me to get there?

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1(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
 4 years ago
Best ResponseYou've already chosen the best response.1seeing how i thought my first explanation was suffieicnt; youll have to address where it is your following goes amiss at

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1dw:1327864212303:dw

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1y = 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
 4 years ago
Best ResponseYou've already chosen the best response.1if we know where the lines meet, we have a point of reference to measure distance with ...dw:1327864376411:dw

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1y = 2x + 3 ( y = 1/2 x)  0 = 5/2 x + 3 ; when x = 3/5

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1y = 1/2 * 3/5 = 3/10 therefore, point of intersection is: (3/2 , 3/10) looks better

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1(3/5 , 3/10) that is

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1dw:1327864617337:dw

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1use distance formula for distance

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1ugh!!, 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
 4 years ago
Best ResponseYou've already chosen the best response.1y = 1/2*6/5 = 6/10 = 3/5 (6/5, 3/5) is the point of intersection .....

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1\[d=\sqrt{(2\frac{6}{5})^2+(1\frac{3}{5})^2}\] \[d=\sqrt{(\frac{10+6}{5})^2+(\frac{53}{5})^2}\] \[d=\sqrt{(\frac{16}{5})^2+(\frac{8}{5})^2}\] \[d=\frac{\sqrt{16^2+8^2}}{5}\]

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1that simplifies to 8sqrt(5)/5

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1327864993315:dw

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0that is what we found?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Why doesn't using the pythagorean theorem work here?

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1it does, but first you need to know 2 points. the given point (2,1) and the intersection of the perped lines

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1once you know the 2 points, the distance formula IS the pythag thrm

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0" 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
 4 years ago
Best ResponseYou've already chosen the best response.1because 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 hitsdw:1327865470057:dw

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1teh y axis has nothing to do with it at all

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0OH, THE POINT OF PERPENDICULAR(ness)? to the point 2,1?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0which is the part where we found the perp. point? that is the next step correct?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0we 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
 4 years ago
Best ResponseYou've already chosen the best response.0until there is an intersection

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0is there an equation to find that point?

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1its solving a system of equations; y = 2x + 3 y = 1/2x we can sub, eliminate, or any other method to solve the sytem

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1it turns out that i used elimination and came up with those fractions

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1y = 1/2 x 2y = x, sub in top y = 2(2y) + 3 y = 4y + 3 5y = 3 y = 3/5

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1knowing y, solve for x

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.13/5 = 1/2 x 2*3/5 = x 6/5 = x

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1those x and y parts are the point of intersection

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ahhh, 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.
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