# Analytic geometry - examples

Also known as coordinate geometry or Cartesian geometry.

1. Vertices of a right triangle Show that the points D(2,1), E(4,0), F(5,7) are vertices of a right triangle.
2. Forces 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.
3. Triangle Triangle KLM is given by plane coordinates of vertices: K[-12, -11] L[-15, -18] M[-13, -12]. Calculate its area and itsinterior angles.
4. Center Calculate the coordinates of the center of gravity T [x, y] of triangle ABC; A[11,4] B[13,-7] C[-17,-18].
5. 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
6. Angle between lines Calculate the angle between these two lines: ? ?
7. Angle between vectors Find the angle between the given vectors to the nearest tenth of a degree. u = (-22, 11) and v = (16, 20)
8. Slope What is the slope of a line with an inclination -221°?
9. Circle 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
10. XY triangle Determine area of triangle given by line 7x+8y-69=0 and coordinate axes x and y.
11. Circle From the equation of a circle: ? Calculate the coordinates of the center of the circle S[x0, y0] and radius of the circle r.
12. Circle Write the equation of a circle that passes through the point [0,6] and touch the X-axis point [5,0]: ?
13. Distance Calculate distance between two points X[18; 19] and W[20; 3].
14. Perpendicular What is the slope of the perpendicular bisector of line segment AB if A[-4,-5] and B[1,-1]?
15. Perpendicular Determine the slope of the line perpendicular to the line p: y = -x +4.
16. Circle Circle is given by centre on S[-7; 10] and maximum chord 13 long. How many intersect points have circle with the coordinate axes?
17. Line 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. Center 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].
19. Center Calculate the coordinates of the circle center: ?
20. Cone 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?

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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.