# Analytic geometry - problems

Also known as coordinate geometry or Cartesian geometry.

1. Find parameters
Find parameters of the circle in the plane - coordinates of center and radius: ?
2. A screen
A screen is 1680 x 1050 pixels. What are the coordinates (and size in pixels) of an centered area which is exactly 33% of the screen size?
3. 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.
4. 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.
5. Center
Calculate the coordinates of the center of gravity T [x, y] of triangle ABC; A[11,4] B[13,-7] C[-17,-18].
6. 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
7. Angle between lines
Calculate the angle between these two lines: ? ?
8. Angle between vectors
Find the angle between the given vectors to the nearest tenth of a degree. u = (-22, 11) and v = (16, 20)
9. Slope
What is the slope of a line with an inclination -221°?
10. 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
11. XY triangle
Determine area of triangle given by line 7x+8y-69=0 and coordinate axes x and y.
12. 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.
13. Circle
Write the equation of a circle that passes through the point [0,6] and touch the X-axis point [5,0]: ?
14. Distance
Calculate distance between two points X[18; 19] and W[20; 3].
15. Perpendicular
What is the slope of the perpendicular bisector of line segment AB if A[-4,-5] and B[1,-1]?
16. Perpendicular
Determine the slope of the line perpendicular to the line p: y = -x +4.
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. 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?
19. 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].
20. Center
Calculate the coordinates of the circle center: ?

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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.