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. Quadrilateral 2
    quadrilateral Show that the quadrilateral with vertices P1(0,1), P2(4,2) P3(3,6) P4(-5,4) has two right triangles.
  2. Vertices of RT
    RightTriangleMidpoint_3 Show that the points P1 (5,0), P2 (2,1) & P3 (4,7) are the vertices of a right triangle.
  3. 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?
  4. Linear independence
    colinear_vectors Determine if vectors u=(3; -3) and v=(0; 3) are linear Linear dependent.
  5. Vector
    vectors Determine coordinates of the vector u=CD if C[13;-8], D[-19,-13].
  6. 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.
  7. 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].
  8. Center
    circle Calculate the coordinates of the circle center: ?
  9. 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.
  10. Distance
    origin_math Wha is the distance between the origin and the point (23; -7)?
  11. Perpendicular
    perpendicular Determine the slope of the line perpendicular to the line p: y = 9x +7.
  12. 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?
  13. Angle between vectors
    arccos Find the angle between the given vectors to the nearest tenth of a degree. u = (24, -1) and v = (12, 16)
  14. 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].
  15. 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?
  16. Distance
    distance Calculate distance between two points Z[7; -9] and U[-10; -8].
  17. 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.
  18. Angle between lines
    angle_two_lines Calculate the angle between these two lines: ? ?
  19. 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?
  20. Slope
    slope What is the slope of a line with an inclination 1.06 rad?

Do you have interesting mathematical example that you can't solve it? Enter it and we can try to solve it.



To this e-mail address we will reply solution; solved examples are also published here. Please enter e-mail correctly and check whether you don't have a full mailbox.