High school + analytic geometry - examples
- Symmetry by plane
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
- Midpoint 4
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?
- Coordinates of midpoint
If the midpoint of the segment is (6,3) and the other end is (8,4) what are the coordinate of the other end?
- Three points
Three points A (-3;-5) B (9;-10) and C (2;k) . AB=AC What is value of k?
- On line
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].
- Center of line segment
Calculate the distance of the point X [1,3] from the center of the line segment x = 2-6t, y = 1-4t ; t is .
- Coordinates of vector
Determine the coordinate of a vector u=CD if C(19;-7) and D(-16;-5)
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.
Triangle KLM is given by plane coordinates of vertices: K[-12, -11] L[-15, -18] M[-13, -12]. Calculate its area and itsinterior angles.
- Speed of Slovakian trains
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
Calculate the coordinates of the center of gravity T [x, y] of triangle ABC; A[11,4] B[13,-7] C[-17,-18].
- Angle between lines
Calculate the angle between these two lines: ? ?
- Angle between vectors
Find the angle between the given vectors to the nearest tenth of a degree. u = (-22, 11) and v = (16, 20)
What is the slope of a line with an inclination -221°?
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
- XY triangle
Determine area of triangle given by line 7x+8y-69=0 and coordinate axes x and y.
From the equation of a circle: ? Calculate the coordinates of the center of the circle S[x0, y0] and radius of the circle r.
Write the equation of a circle that passes through the point [0,6] and touch the X-axis point [5,0]: ?
Calculate distance between two points X[18; 19] and W[20; 3].
What is the slope of the perpendicular bisector of line segment AB if A[-4,-5] and B[1,-1]?
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.