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# distance between parallel lines formula

Question:I don't want the formula. I want to know how to prove the formula. Please show me. If can't, link me useful website. However not wikipedia. :) Thanks in advance. This is an assignment. The lecture want me to prove the formula.

Answers:I don't understand. What are you trying ot prove? The distance between two parallel lines is uniform? Two parallel lines are always equidistant between each other, between any two points on the lines that are directly in line with each other. I don't get the question.

Question:Find the distance between each pair of parallel lines. y=4x y=4x-17 First I graphed the problem and drew a perpendicular line from on of the points on another line and the slope of the perpendicular line is - 1/4. then i used the system of equations and y=17. I am not sure where to go from there. Please help and explain. Thank you in advance

Answers:You need to find the distance along the y axis (which is 17 in this case) and the distance along the x axis (hint: set y = 0 in the bottom equation since the first equation goes through the origin). The distance between the lines will be the square root of the sum of the squares of these x and y distances (do you recognize the application of the Pythagorean theorem?).

Question:I've been doing a lot of homework and I am almost done. I just need to do this one problem. The question is "What is the distance between parallel lines whose equations are Y=2x+7 and Y=2x-3?" Thanks in advance. :D

Answers:Easy: Get the line perpendicular to them both, which has its gradient as -1/gradient of the 2 lines. Since both lines have the same gradient, then we can use any line: If we compare y = 2x + 7 to y = mx + c, where m is the gradient and c is the y-intercept, then we can safely say that the gradient is 2, so the gradient of the perpendicular line is -0.5. Using y = mx + c, we can say that the perpendicular line is y = -0.5 + c, and c can be any number because it will still intersect both the 2 lines at 90 degrees. So for simplicity, we will say that c = 0. So the equation is y = -0.5x. So now, to find the distance, we need to find the two points of intersection, and calculate the distance from them, so we will see the points of intersection of: y = 2x + 7 and y = -0.5x: at intersection the y will be equal for both equations. So we will say that 2x + 7 = -0.5x , and from there we will find that x = -2.8, which corresponds to y =1.4. So the first coordinates are (-2.8,1.4). If we do the same to the other equation, we will get the coordinates (1.2,-0.6). So to find the distance between them, we use the equation(\/ is the square root): dist=\/((x2-x1)^2 - (y2-y1)^2), then the distance will be \/18 = 4.24. And you're welcome :)

Question:If I had the parallel lines y=2x+2 and y=2x-3, how do I find the distance between the 2 lines? Please show your work and explain in words how you solved the problem. Thanks. We're not allowed to make a graph and graph the lines.

Answers:Since the lines are parallel all the points on one line are the same distance to the other line. So pick any point on one line and calculate the distance to the other line. y = 2x + 2 y = 2x - 3 Pick the point P(1, 4) on the first line and calculate the distance to the second line. d = | 2*1 - 1*4 - 3 | / [2 + (-1) ] = 5/ 5 = 5