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Does any one know how to find the distance between the point (2,3) and the line 4x + 3y = 10?
 one year ago
 one year ago
Does any one know how to find the distance between the point (2,3) and the line 4x + 3y = 10?
 one year ago
 one year ago

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mathstudent55Best ResponseYou've already chosen the best response.1
First, find the equation of the line perpendicular to the given line that passes thorugh (2, 3). Once you have the equation of the perpendicular, solve a system of equations of the two equations to find where the lines intersect. Then, find the distance between the point of intersection and point (2, 3).
 one year ago

LucyLu15Best ResponseYou've already chosen the best response.1
Could x=2 @mathstudent55
 one year ago

Matt.MawsonBest ResponseYou've already chosen the best response.0
Ok this is a big pain to solve, but here it is. First put the equation of the line into y = m*x+b format y = (4/3)x + 3.333 The perpendicular line will have slope 3/4 and passes through (2,3) so it's equation will be y = (3/4)x+4.5 The two lines intersect at (.56,4.08) The triangle with tip (.56,4.08) and right point at (2,3) has base 1.44 and height of 1.08 \[\sqrt{1.44^{2}+1.08^{2}} = 1.8 \] 1.8 is the answer
 one year ago

LucyLu15Best ResponseYou've already chosen the best response.1
when they intersect i get (2,6)?
 one year ago

mathstudent55Best ResponseYou've already chosen the best response.1
What did you get for the equation of the perpendicular?
 one year ago

LucyLu15Best ResponseYou've already chosen the best response.1
i plugged in the one that you had calculated
 one year ago

mathstudent55Best ResponseYou've already chosen the best response.1
@Matt.Mawson calculated it, but I think he made a mistake.
 one year ago

mathstudent55Best ResponseYou've already chosen the best response.1
Let's start from the beginning. The given line is: 4x + 3y = 10
 one year ago

mathstudent55Best ResponseYou've already chosen the best response.1
Solve it for y to get the slope: 3y = 4x + 10 y = (4/3)x + 10/3
 one year ago

mathstudent55Best ResponseYou've already chosen the best response.1
He made a mistake right in the beginning when he subtracted the 4x from both sides. It should be 4x on the right side, but he wrote 4x.
 one year ago

LucyLu15Best ResponseYou've already chosen the best response.1
Yes i get that for my equation as well. and for my perpendicular i calculated y=(3/4)x +1.5
 one year ago

mathstudent55Best ResponseYou've already chosen the best response.1
Yes, I have both of those.
 one year ago

LucyLu15Best ResponseYou've already chosen the best response.1
for my point of intercept i have .88, 2.16
 one year ago

mathstudent55Best ResponseYou've already chosen the best response.1
Yes, I got the same x and y as you.
 one year ago

LucyLu15Best ResponseYou've already chosen the best response.1
so how will i find the distance?
 one year ago

mathstudent55Best ResponseYou've already chosen the best response.1
The final step is the distance between (0.88, 2.16) and (2,3)
 one year ago

mathstudent55Best ResponseYou've already chosen the best response.1
For that distance I get 1.4
 one year ago

LucyLu15Best ResponseYou've already chosen the best response.1
yes i have that too... Okay. Thank You!
 one year ago
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