Analytic geometry - examples

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.

  1. Line
    img2 Line p passing through A[-10, 1] and has direction vector v=(2, 4). Is point B[-20, -19] on the line p?
  2. Linear independence
    colinear_vectors Determine if vectors u=(3; -3) and v=(0; 3) are linear Linear dependent.
  3. Vector
    vectors Determine coordinates of the vector u=CD if C[13;-8], D[-19,-13].
  4. Lie/do not lie
    lines_and_points The function is given by the rule f(x) = -x-12. Determine whether point D[-4; 2] lies on this function. Solve graphically or numerically and give reasons for the your answer.
  5. Center
    triangle_axis Calculate the coordinates of the center of gravity T [x, y] of triangle ABC; A[27,-11] B[2,-30] C[11,12].
  6. 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.
  7. Center
    circle Calculate the coordinates of the circle center: ?
  8. Distance
    origin_math Wha is the distance between the origin and the point (23; -7)?
  9. Circle
    circles_2 Circle is given by centre on S[-9; 4] and maximum chord 20 long. How many intersect points have circle with the coordinate axes?
  10. Perpendicular
    perpendicular Determine the slope of the line perpendicular to the line p: y = 9x +7.
  11. Segment
    segment_AB Calculate the length of the segment AB, if the coordinates of the end vertices are A[-2, -4] and B[-5, -1].
  12. Distance
    distance Calculate distance between two points Z[7; -9] and U[-10; -8].
  13. Midpoint of segment
    midpoint-segment Point A has coordinates [15; 1] and the midpoint of the segment AB is the point [-20; 13]. What are the coordinates of point B?
  14. 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.
  15. Angle between lines
    angle_two_lines Calculate the angle between these two lines: ? ?
  16. Diameter
    diameter_circle If the endpoints of a diameter of a circle are A(10, -5) and B (8, 7), what is the radius of the circle?
  17. Slope
    lines.JPG Calculate the slope of a line that intersects points (38,-23) and (-93,5).
  18. Slope
    slope What is the slope of a line with an inclination 1.06 rad?
  19. Line
    lines_1 Write an equation of a line parallel to To 9x + 3y = 8 That Passes Through The Point (-1, -4). Write in form ax+by=c.
  20. The angle of lines
    lines Calculate the angle of two lines y=-3x+25 and y=x-3

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