# Analytic geometry + Pythagorean theorem - examples

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. 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. Angle between vectors
Find the angle between the given vectors to the nearest tenth of a degree. u = (-22, 11) and v = (16, 20)
5. 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
6. Circle
Write the equation of a circle that passes through the point [0,6] and touch the X-axis point [5,0]: ?
7. Distance
Calculate distance between two points X[18; 19] and W[20; 3].
8. Center
Calculate the coordinates of the circle center: ?
9. Segment
Calculate the length of the segment AB, if the coordinates of the end vertices are A[10, -4] and B[5, 5].
10. Unit vector 2D
Determine coordinates of unit vector to vector AB if A[-6; 8], B[-18; 10].
11. Diameter
If the endpoints of a diameter of a circle are A(10, -1) and B (3, 10), what is the radius of the circle?
4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall?
13. Square side
Calculate length of side square ABCD with vertex A[0, 0] if diagonal BD lies on line p: -4x -5 =0.
14. Distance
Wha is the distance between the origin and the point (18; 22)?
15. 3d vector component
The vector u = (3.9, u3) and the length of the vector u is 12. What is is u3?
16. Vertices of RT
Show that the points P1 (5,0), P2 (2,1) & P3 (4,7) are the vertices of a right triangle.
17. Right angled triangle 2
LMN is a right angled triangle with vertices at L(1,3), M(3,5) and N(6,n). Given angle LMN is 90° find n
18. Right triangle - leg
Calculate to the nearest tenth cm length of leg in right-angled triangle with hypotenuse length 9 cm and 7 cm long leg.
19. Inscribed circle
Write the equation of a incircle of the triangle KLM if K [2,1], L [6,4], M [6,1].
20. Triangle IRT
In isosceles right triangle ABC with right angle at vertex C is coordinates: A (-1, 2); C (-5, -2) Calculate the length of segment AB.

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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. Pythagorean theorem is the base for the right triangle calculator. See also more information on Wikipedia.