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LucyLu15
 2 years ago
Does any one know how to find the distance between the point (2,3) and the line 4x + 3y = 10?
LucyLu15
 2 years ago
Does any one know how to find the distance between the point (2,3) and the line 4x + 3y = 10?

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mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1First, 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).

LucyLu15
 2 years ago
Best ResponseYou've already chosen the best response.1Could x=2 @mathstudent55

Matt.Mawson
 2 years ago
Best ResponseYou've already chosen the best response.0Ok 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

LucyLu15
 2 years ago
Best ResponseYou've already chosen the best response.1when they intersect i get (2,6)?

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1What did you get for the equation of the perpendicular?

LucyLu15
 2 years ago
Best ResponseYou've already chosen the best response.1i plugged in the one that you had calculated

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1@Matt.Mawson calculated it, but I think he made a mistake.

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1Let's start from the beginning. The given line is: 4x + 3y = 10

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1Solve it for y to get the slope: 3y = 4x + 10 y = (4/3)x + 10/3

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1He 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.

LucyLu15
 2 years ago
Best ResponseYou've already chosen the best response.1Yes i get that for my equation as well. and for my perpendicular i calculated y=(3/4)x +1.5

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1Yes, I have both of those.

LucyLu15
 2 years ago
Best ResponseYou've already chosen the best response.1for my point of intercept i have .88, 2.16

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1Yes, I got the same x and y as you.

LucyLu15
 2 years ago
Best ResponseYou've already chosen the best response.1so how will i find the distance?

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1The final step is the distance between (0.88, 2.16) and (2,3)

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1For that distance I get 1.4

LucyLu15
 2 years ago
Best ResponseYou've already chosen the best response.1yes i have that too... Okay. Thank You!
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