Analytic geometry - problems

Also known as coordinate geometry or Cartesian geometry.

  1. Forces
    ijk In point O acts three orthogonal forces: F1 = 20 N, F2 = 7 N and F3 = 19 N. Determine the resultant of F and the angles between F and forces F1, F2 and F3.
  2. Triangle
    sedlo Triangle KLM is given by plane coordinates of vertices: K[-12, -11] L[-15, -18] M[-13, -12]. Calculate its area and itsinterior angles.
  3. Speed of Slovakian trains
    zssk_train Rudolf decided to take the train from the station 'Trnava' to 'Zemianske Kostoľany'. In the train timetables found train R 725 Remata : km0Bratislava hl.st.12:574Bratislava-Vinohrady13:0113:0219Pezinok13:1213:1346Trnava13:3013:3263Leopoldov13:4514:0168H
  4. Center
    triangle_axis Calculate the coordinates of the center of gravity T [x, y] of triangle ABC; A[11,4] B[13,-7] C[-17,-18].
  5. Angle between lines
    angle_two_lines Calculate the angle between these two lines: ? ?
  6. Angle between vectors
    arccos Find the angle between the given vectors to the nearest tenth of a degree. u = (-22, 11) and v = (16, 20)
  7. Slope
    slope What is the slope of a line with an inclination -221°?
  8. Circle
    kruznica Circle touch two parallel lines p and q; and its center lies on a line a, which is secant of lines p and q. Write the equation of circle and determine the coordinates of the center and radius. p: x-10 = 0 q: -x-19 = 0 a: 9x-4y+5 = 0
  9. XY triangle
    triangle Determine area of triangle given by line 7x+8y-69=0 and coordinate axes x and y.
  10. Circle
    circles From the equation of a circle: ? Calculate the coordinates of the center of the circle S[x0, y0] and radius of the circle r.
  11. Circle
    circle_ag Write the equation of a circle that passes through the point [0,6] and touch the X-axis point [5,0]: ?
  12. Distance
    distance Calculate distance between two points X[18; 19] and W[20; 3].
  13. Perpendicular
    slopeplane What is the slope of the perpendicular bisector of line segment AB if A[-4,-5] and B[1,-1]?
  14. Perpendicular
    perpendicular Determine the slope of the line perpendicular to the line p: y = -x +4.
  15. Circle
    circles_2 Circle is given by centre on S[-7; 10] and maximum chord 13 long. How many intersect points have circle with the coordinate axes?
  16. Line
    negative_slope Straight line passing through points A [-3; 22] and B [33; -2]. Determine the total number of points of the line which both coordinates are positive integers.
  17. Center
    circle Calculate the coordinates of the circle center: ?
  18. Cone
    cones_1 If the segment of the line y = -3x +4 that lies in quadrant I is rotated about the y-axis, a cone is formed. What is the volume of the cone?
  19. Center
    center_triangle In the triangle ABC is point D[1,-2,6], which is the center of the |BC| and point G[8,1,-3], which is the center of gravity of the triangle. Find the coordinates of the vertex A[x,y,z].
  20. Line
    img2 Line p passing through A[-10, 6] and has direction vector v=(3, 2). Is point B[7, 30] on the line p?

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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. See also more information on Wikipedia.