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 result:

x =  9
y =  6

Solution:

3x4y3=0  x=(3+4y)/3=9 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 3x-4y-3=0 \ \\ \ \\ x=(3+4y)/3=9 \ \\ y=(3x-3)/4 \ \\ |AC|=|BC| \ \\ \ \\ (x-4)^2+(y-4)^2=(x-7)^2+(y-1)^2 \ \\ \ \\ (x-4)^2+((3x-3)/4-4)^2=(x-7)^2+((3x-3)/4-1)^2 \ \\ 1.5x=13.5 \ \\ \dfrac{ 3 }{ 2 }x=\dfrac{ 27 }{ 2 } \ \\ 3x=27 \ \\ x=27 / 3=9 \ \\
y=(3x3)/4=(3 93)/4=6y=(3x-3)/4=(3 \cdot \ 9-3)/4=6



Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!





Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

Showing 0 comments:
avatar




Tips to related online calculators
For Basic calculations in analytic geometry is helpful line slope calculator. From coordinates of two points in the plane it calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of segment, intersections 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 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

Next similar math problems:

  • 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
  • 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].
  • Parametric equation
    line Find the parametric equation of a line with y-intercept (0,-4) and a slope of -2.
  • Roots and coefficient
    parabola In the equation 2x ^ 2 + bx-9 = 0 is one root x1 = -3/2. Determine the second root and the coefficient b.
  • Discriminant
    Quadratic_equation_discriminant Determine the discriminant of the equation: ?
  • Roots
    parabola Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
  • Equation
    calculator_2 Equation ? has one root x1 = 8. Determine the coefficient b and the second root x2.
  • Equation with abs value
    abs_graph How many solutions has the equation ? in the real numbers?
  • Equation of circle
    circle_analytics find an equation of the circle with indicated properties: a. center at (-3,5), diameter 20. b. center at origin and diameter 16.
  • Circle - AG
    circle2 Find the coordinates of circle and its diameter if its equation is: ?
  • Square root 2
    parabola_2 If the square root of 3m2 +22 and -x = 0, and x=7, what is m?
  • Equation 23
    reciprocal_1 Find value of unknown x in equation: x+3/x+1=5 (problem finding x)
  • Evaluation of expressions
    eq222_10 If a2-3a+1=0, find (i)a2+1/a2 (ii) a3+1/a3
  • Reciprocal value
    fx How do I calculate a number x that is 9 greater than its reciprocal (1/x)?
  • Solve equation
    hrusky_2 solve equation: ?
  • Quadratic equation
    kvadrat_2 Find the roots of the quadratic equation: 3x2-4x + (-4) = 0.
  • Solve 3
    eq2_4 Solve quadratic equation: (6n+1) (4n-1) = 3n2