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.
- Points on line segment
Points P & Q belong to segment AB. If AB=a, AP = 2PQ = 2QB, find the distance: between point A and the midpoint of the segment QB.
- 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
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 52°?
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.
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