equidistant Definition and 20 Threads

All points on that line are equidistant from the points a and b. Thus, the length of ##\frac {z - a} {z - b}## is 1, i.e., the points on the unit circle. If the angle of ##z - a## is ##\alpha##, and the angle of ##z - b## is ##\beta##, then the angle of ##\frac {z - a} {z - b}## is ##\alpha -...

Hi, i'm trying to solve this problem. It's exercise 3 on page 5 from this book: Challenging mathematical problem with elementary solutions The solution is on page 41: I'm OK with the 4 circles in case 1: i can pick (inside/outside): ABC + D, ABD + C, ADC + B, BCD + A. What i cannot...

Does there exist a binary fractal tree… (reference: http://ecademy.agnesscott.edu/~lriddle/ifs/pythagorean/symbinarytree.htm ) …whose leaves (endpoints) lie on a circle and are equidistant? Consider a binary fractal tree with branches decreasing in length by a scaling factor r (0 < r < 1) for...

Homework Statement This problem is taken from S L Loney Coordinate geometry exercise (ch 2)[/B] Prove that a point can be found which is at the same distance from each of the four points ## \bigg(am_1,\dfrac{a}{m_1}\bigg),\bigg(am_2,\dfrac{a}{m_2}\bigg),\bigg(am_3,\dfrac{a}{m_3}\bigg) ## and...

Homework Statement In the figure the four particles form a square of edge length a = 6.10 cm and have charges q1 = 6.35 nC, q2 = -17.9 nC, q3 = 17.9 nC, and q4 = -6.35 nC. What is the magnitude of the net electric field produced by the particles at the square's center? Homework Equations...

(I assume that the three section headings below form the template referred to below) 1. Homework Statement n identical equi-distant particles are distributed equi-distantly around the circumference of a ring of radius r in space. Each particles is of mass m, so the total mass of the ring is...

If we are asked to place 3 points on the surface of a sphere so that they are equidistant, it's easy to visualize that the result will be such that the three points form an equilateral triangle. If asked to place 4 points it's easy to visualize that the result is such that the points arrange...

Homework Statement Find the equation of the plane parallel to 2x - y + 2z = 4 if the point P = (3,2,-1) is equidistant from both planes. Homework Equations a(x-x0) + b(y-y0) + c(z-z0) = 0 The Attempt at a Solution I found the normal vector to the given plane first, as this is quite easy...

Homework Statement In Fig.22-30, the four particles form a square of edge length a = 6.50 cm and have charges q1 = 7.59 nC, q2 = -10.9 nC, q3 = 11.5 nC, and q4 = -6.06 nC. What is the magnitude of the net electric field produced by the particles at the square's center...

Hello all, Could someone help me out with this problem? I tried using circle geometries, perpendicular bisectors, and some more pure algebra. Nothing has been "unifying." Here is the problem: Is it possible to have a point Q=(r,s), where r and s are rational, where the point Q is not...

Draw an ellipse. Then draw a curve that is equidistant all the way around the outside of the ellipse. Is that new curve also an ellipse? I've drawn it out and I can show examples where it's obviously not an ellipse, but I can't come up with a good non-visual explanation. I thought that maybe...

Homework Statement I need the formula for finding the coordinates of the point on the y-axis that are equildistant from two other pair of points (3,0) and (3,6). Homework Equations i don't know, but these might have something to do with it. \sqrt{} (y2-y1)2+(x2-x1)2 (x2+x1/2...

Homework Statement Find an equation of the set of all points equidistant from the points A(-1,5,3) and B(6,2,-2). Describe the set Homework Equations dot product cross product The Attempt at a Solution the book found the line: 14x - 6y - 10z = 9 which is perpendicular and i guess...

Homework Statement Find an equation of the set of all points equidistant from the set points A(-1,5,3) and B(6,2,-2). Describe the set. Homework Equations d= sqrt [(x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2] The Attempt at a Solution I solved the distance between A and B and got d=sqrt...

Homework Statement Find the equation of a plane, every point of which is equidistant from the points A(1, 1, 0) and B(5, 3, -2) The Attempt at a Solution I am quite stuck... I wasn't sure if I could find vectors AP and BP and then find their magnitudes using square root x^2 + y^2 + z^2

Homework Statement Find an equation of the set of all points equidistant from the points A(-1,5,3) and B(6,2,-2). Describe the set. Homework Equations None... The Attempt at a Solution Um, I've drawn a graph of the two points and that's about as far as I could get. I know the...

I got two points that are (2, -1, 1) and (3, 1, 5) and I need to find the equation of the plane equidistant from those points. Anyone?

1. Find the coordinates of the point on the line y=3x+1 that is equidistant from (0,0) and (-3,4) 2. distance formula 3. I have no idea how to do this. X_X

I need help. I am not getting the solution to this: A curve passes through the point (1,1) and has the property that the normal at any point on the curve is equidistant from the x-axis and the origin. Form the differential equation for the curve, find the curve and state which quadrant(s) the...

How would you do this question determine the equation of the locus Locus whose points are equidistant from the x and y axis? :cry: I HATE LOCUS!