On a line

On a line p : 3 x - 4 y - 3 = 0, determine the point C equidistant from points A[4, 4] and B[7, 1].

Correct answer:

x =  9
y =  6

Step-by-step explanation:

3x4y3=0  x=(3+4y)/3 y=(3x3)/4 AC=BC  (x4)2+(y4)2=(x7)2+(y1)2  (x4)2+((3x3)/44)2=(x7)2+((3x3)/41)2 1.5x=13.5 32x=272 3x=27 x=27/3=9
y=(3x3)/4=(3 93)/4=6



Did you find an error or inaccuracy? Feel free to write us. Thank you!



avatar







Tips to related online calculators
Line slope calculator is helpful for basic calculations in analytic geometry. The coordinates of two points in the plane calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of the segment, intersections of the coordinate axes, etc.
Looking for help with calculating roots of a quadratic equation?
Do you have a linear equation or system of equations and looking for its solution? Or do you have a quadratic equation?
Pythagorean theorem is the base for the right triangle calculator.

 
We encourage you to watch this tutorial video on this math problem: video1   video2

Related math problems and questions:

  • Sphere equation
    sphere2.jpg Obtain the equation of sphere its centre on the line 3x+2z=0=4x-5y and passes through the points (0,-2,-4) and (2,-1,1).
  • On line
    primka On line p: x = 4 + t, y = 3 + 2t, t is R, find point C, which has the same distance from points A [1,2] and B [-1,0].
  • Calculate 6
    distance_point_line Calculate the distance of a point A[0, 2] from a line passing through points B[9, 5] and C[1, -1].
  • Circle
    kruznica The circle touches two parallel lines p and q, and its center lies on line a, which is the secant of lines p and q. Write the equation of the circle and determine the coordinates of the center and radius. p: x-10 = 0 q: -x-19 = 0 a: 9x-4y+5 = 0
  • Rectangle 39
    rectnagles Find the perimeter and area of the rectangular with vertices (-1, 4), (0,4), (0, -1), and (-4, 4)
  • Symmetry by plane
    roviny Determine the coordinates of a image of point A (3, -4, -6) at a symmetry that is determined by the plane x-y-4z-13 = 0
  • Sphere from tree points
    sphere2 Equation of sphere with three point (a,0,0), (0, a,0), (0,0, a) and center lies on plane x+y+z=a
  • Perpendicular projection
    lines Determine the distance of a point B[1, -3] from the perpendicular projection of a point A[3, -2] on a straight line 2 x + y + 1 = 0.
  • Vectors abs sum diff
    vectors_sum0 The vectors a = (4,2), b = (- 2,1) are given. Calculate: a) |a+b|, b) |a|+|b|, c) |a-b|, d) |a|-|b|.
  • Isosceles triangle
    rr_triangle3 In an isosceles triangle ABC with base AB; A [3,4]; B [1,6] and the vertex C lies on the line 5x - 6y - 16 = 0. Calculate the coordinates of vertex C.
  • Vertices of a right triangle
    right_triangle Show that the points D(2,1), E(4,0), F(5,7) are vertices of a right triangle.
  • Distance problem
    linear_eq A=(x, x) B=(1,4) Distance AB=√5, find x;
  • General line equations
    lines In all examples, write the GENERAL EQUATION OF a line that is given in some way. A) the line is given parametrically: x = - 4 + 2p, y = 2 - 3p B) the line is given by the slope form: y = 3x - 1 C) the line is given by two points: A [3; -3], B [-5; 2] D) t
  • Space vectors 3D
    vectors The vectors u = (1; 3; -4), v = (0; 1; 1) are given. Find the size of these vectors, calculate the angle of the vectors, the distance between the vectors.
  • Three points 4
    linearna The line passed through three points - see table: x y -6 4 -4 3 -2 2 Write line equation in y=mx+b form
  • Coordinates
    geodet Determine the coordinates of the vertices and the content of the parallelogram, the two sides of which lie on the lines 8x + 3y + 1 = 0, 2x + y-1 = 0 and the diagonal on the line 3x + 2y + 3 = 0
  • Three points
    abs1 Three points A (-3;-5) B (9;-10) and C (2;k) . AB=AC What is value of k?