Analytic geometry + Pythagorean theorem - math problems

Also known as coordinate geometry or Cartesian geometry.

  1. Angle of the body diagonals
    body_diagonals_angle Using vector dot product calculate the angle of the body diagonals of the cube.
  2. Suppose
    linear_eq Suppose you know that the length of a line segment is 15, x2=6, y2=14 and x1= -3. Find the possible value of y1. Is there more than one possible answer? Why or why not?
  3. A cell tower
    tower A cell tower is located at coordinates (-5, -7) and has a circular range of 12 units. If Mr. XYZ is located at coordinates (4,5), will he be able to get a signal?
  4. Parametric form
    vzdalenost Calculate the distance of point A [2,1] from the line p: X = -1 + 3 t Y = 5-4 t Line p has a parametric form of the line equation. ..
  5. Coordinates of square vertices
    rotate_square I have coordinates of square vertices A / -3; 1/and B/1; 4 /. Find coordinates of vertices C and D, C 'and D'. Thanks Peter.
  6. Distance between 2 points
    axes2 Find the distance between the points (7, -9), (-1, -9)
  7. Touch x-axis
    touch_circle Find the equations of circles that pass through points A (-2; 4) and B (0; 2) and touch the x-axis.
  8. Find parameters
    circle_axes_1 Find parameters of the circle in the plane - coordinates of center and radius: ?
  9. Vertices of a right triangle
    right_triangle_5 Show that the points D(2,1), E(4,0), F(5,7) are vertices of a right triangle.
  10. Three points
    abs1_1 Three points A (-3;-5) B (9;-10) and C (2;k) . AB=AC What is value of k?
  11. 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].
  12. Center of line segment
    stredna_priecka_1 Calculate the distance of the point X [1,3] from the center of the line segment x = 2-6t, y = 1-4t ; t is .
  13. Distance problem 2
    geodetka_1 A=(x,2x) B=(2x,1) Distance AB=√2, find value of x
  14. Distance problem
    linear_eq_3 A=(x, x) B=(1,4) Distance AB=√5, find x;
  15. Find the 5
    distance-between-point-line Find the equation with center at (1,20) which touches the line 8x+5y-19=0
  16. Two people
    crossing Two straight lines cross at right angles. Two people start simultaneously at the point of intersection. John walking at the rate of 4 kph in one road, Jenelyn walking at the rate of 8 kph on the other road. How long will it take for them to be 20√5 km apa
  17. Right triangle from axes
    axes2 A line segment has its ends on the coordinate axes and forms with them a triangle of area equal to 36 square units. The segment passes through the point ( 5,2). What is the slope of the line segment?
  18. Prove
    two_circles_1 Prove that k1 and k2 is the equations of two circles. Find the equation of the line that passes through the centers of these circles. k1: x2+y2+2x+4y+1=0 k2: x2+y2-8x+6y+9=0
  19. Hyperbola
    hyperbola Find the equation of hyperbola that passes through the point M [30; 24] and has focal points at F1 [0; 4 sqrt 6], F2 [0; -4 sqrt 6].
  20. Ellipse
    elipsa Ellipse is expressed by equation 9x2 + 25y2 - 54x - 100y - 44 = 0. Find the length of primary and secondary axes, eccentricity, and coordinates of the center of the ellipse.

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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. Pythagorean theorem is the base for the right triangle calculator. See also more information on Wikipedia.