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.
In point X acts three orthogonal forces: F1 = 13 N, F2 = 8 N and F3 = 15 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[-19, -8] L[8, -12] M[2, -6]. Calculate its area and itsinterior angles.
Calculate the coordinates of the center of gravity T [x, y] of triangle ABC; A[27,-11] B[2,-30] C[11,12].
- Speed of Slovakian trains
Rudolf decided to take the train from the station 'Nová Baňa' to 'Gelnica'. In the train timetables found train R 371 Horehronec : km0Břeclav os.n.05:268Lanžhot05:3205:3214Brodské05:3705:3818Kúty05:4205:4344Malacky05:5906:0082Bratislava hl.st.06:2606:37
- Angle between lines
Calculate the angle between these two lines: ? ?
What is the slope of a line with an inclination 1.06 rad?
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+3y+1 = 0 q: x-3y-1 = 0 a: -10x-3y-2 = 0
- Angle between vectors
Find the angle between the given vectors to the nearest tenth of a degree. u = (24, -1) and v = (12, 16)
- XY triangle
Determine area of triangle given by line -7x+7y+63=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 [0,8] and touch the X-axis point [2,0]: ?
Calculate distance between two points Z[7; -9] and U[-10; -8].
What is the slope of the perpendicular bisector of line segment AB if A[-9,-8] and B[-8,0]?
Circle is given by centre on S[-9; 4] and maximum chord 20 long. How many intersect points have circle with the coordinate axes?
Calculate the coordinates of the circle center: ?
If the segment of the line y = -8x +4 that lies in quadrant I is rotated about the y-axis, a cone is formed. What is the volume of the cone?
In the triangle ABC is point D[-8,-9,9], which is the center of the |BC| and point G[5,9,5], which is the center of gravity of the triangle. Find the coordinates of the vertex A[x,y,z].
Determine the slope of the line perpendicular to the line p: y = 9x +7.
- Linear independence
Determine if vectors u=(3; -3) and v=(0; 3) are linear Linear dependent.
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.
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