find the distance from (3,5) to 4x+3y=2
2006-10-19 14:09:38 · 6 answers · asked by kyle w 1 in Science & Mathematics ➔ Mathematics
shortest distance between point and line
2006-10-19 14:17:55 · update #1
doesn't really make sense, (3,5) is a point, and 4x+3y=2 is an equation.
2006-10-19 14:14:54 · answer #1 · answered by this Mike guy 5 · 1⤊ 0⤋
The shortest distance is from (3,5) along a line perpendicular to the given line to the point where the two lines intersect.
Find the slope of the given line
4x + 3y = 2
3y = -4x + 2
y = -4x/3 + 2/3
The slope of the line is -4/3, so the slope of the perpendicular line is the negative reciprocal, or 3/4.
The equation of the perpendicular line using the given point.
5 = 3(3)/4 + b
5 - 9/4 = b
11/4 = b
y = 3x/4 + 11/4
Both solved for y, set = to each other
-4x/3 + 2/3 = 3x/4 + 11/4
-16x + 8 = 9x + 33
-25x = 25
x = -1
y = -4(-1)/3 + 2/3
y = 4/3 + 2/3
y = 2
The lines intersect at (-1, 2)
the distance between the points is
d = sqrt[(5 - 2)^2 + (3 -(-1))^2]
d = sqrt[9 + 16]
d = 5
2006-10-19 22:46:30 · answer #2 · answered by kindricko 7 · 0⤊ 0⤋
4x + 3y = 2 has an infinite number of solutions. If you want the shortest distance between the point and the line, thats something entirely different and you should say so.
2006-10-19 21:12:45 · answer #3 · answered by davidosterberg1 6 · 0⤊ 0⤋
12+15-2/(rt(25)
=25/5=5 units
2006-10-19 21:12:11 · answer #4 · answered by raj 7 · 1⤊ 0⤋
(4(3)+3(5)-2)/sqrt(25)
2006-10-19 21:12:46 · answer #5 · answered by cmadame 3 · 1⤊ 0⤋
If you had asked a little more politely .....Rather curt, don't you think?
2006-10-19 21:11:26 · answer #6 · answered by I am Sunshine 6 · 0⤊ 0⤋