Finding Points on a Line in Slope-Intercept FormDate: 07/29/2005 at 13:24:37 From: Ben Subject: How to find the other two points on a line Hi, Dr. Math: I have a line y = kx + b, and I know point A(x1, x2) is on the line. If point B is also on the line, and the distance between A and B is d, what are the point(s) B? Thanks, Ben Date: 07/29/2005 at 15:17:16 From: Doctor Jaffee Subject: Re: How to find the other two points on a line Hi Ben, Here's how I solved this problem. I drew a line with the point A(x1, x2) on it and a point B(z1,z2). Actually, there are two possible locations for point B. One is to the right and above (if k is a positive number) and the other is to the left and below. If k is negative, then B could be to the right and below A or to the left and above A. Of course, if k is 0, then the problem is easy to solve. If k = 0, the line is horizontal, so all that you have to do is add d to x1 to get z1 and z2 stays the same. Then, subtract d from x1 to find the other point. But, if the line is not horizontal, you have to work a little harder. Assume that the horizontal distance from A to B is p and the vertical distance from A to B is q. Then, the slope of the line is q/p = k. According to the Pythagorean Theorem p^2 + q^2 = d^2. Now, the values for k and d are constants, so solve this system of equations for q and p and you can then easily determine both locations for B. Give it a try and you have any difficulties or you have questions about my suggestions, write back and I'll try to help you some more. Good Luck, - Doctor Jaffee, The Math Forum http://mathforum.org/dr.math/ Date: 07/29/2005 at 15:25:25 From: Ben Subject: Thank you (How to find the other two points on a line) Thanks Doctor Jaffee! That helps a lot! |
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