High school + analytic geometry - examples

  1. 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
  2. Midpoint 4
    segment_3 If the midpoint of a segment is (6,3) and the other end point is (8,-4) what are thw coordinate of the other end?
  3. Coordinates of midpoint
    linear_eq_4 If the midpoint of the segment is (6,3) and the other end is (8,4) what are the coordinate of the other end?
  4. Three points
    abs1_1 Three points A (-3;-5) B (9;-10) and C (2;k) . AB=AC What is value of k?
  5. 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].
  6. 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 .
  7. Coordinates of vector
    vectors_2 Determine the coordinate of a vector u=CD if C(19;-7) and D(-16;-5)
  8. 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.
  9. 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.
  10. 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
  11. 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].
  12. Angle between lines
    angle_two_lines Calculate the angle between these two lines: ? ?
  13. 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)
  14. Slope
    slope What is the slope of a line with an inclination -221°?
  15. 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
  16. XY triangle
    triangle Determine area of triangle given by line 7x+8y-69=0 and coordinate axes x and y.
  17. 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.
  18. Circle
    circle_ag Write the equation of a circle that passes through the point [0,6] and touch the X-axis point [5,0]: ?
  19. Distance
    distance Calculate distance between two points X[18; 19] and W[20; 3].
  20. Perpendicular
    slopeplane What is the slope of the perpendicular bisector of line segment AB if A[-4,-5] and B[1,-1]?

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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.