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.
Line p passing through A[-10, 1] and has direction vector v=(2, 4). Is point B[-20, -19] on the line p?
- Linear independence
Determine if vectors u=(3; -3) and v=(0; 3) are linear Linear dependent.
Determine coordinates of the vector u=CD if C[13;-8], D[-19,-13].
- Lie/do not lie
The function is given by the rule f(x) = -x-12. Determine whether point D[-4; 2] lies on this function. Solve graphically or numerically and give reasons for the your answer.
- Angle between vectors
Find the angle between the given vectors to the nearest tenth of a degree. u = (24, -1) and v = (12, 16)
Calculate the coordinates of the center of gravity T [x, y] of triangle ABC; A[27,-11] B[2,-30] C[11,12].
Calculate the coordinates of the circle center: ?
- Vertices of RT
Show that the points P1 (5,0), P2 (2,1) & P3 (4,7) are the vertices of a right triangle.
From the equation of a circle: ? Calculate the coordinates of the center of the circle S[x0, y0] and radius of the circle r.
Wha is the distance between the origin and the point (23; -7)?
Circle is given by centre on S[-9; 4] and maximum chord 20 long. How many intersect points have circle with the coordinate axes?
Determine the slope of the line perpendicular to the line p: y = 9x +7.
- Midpoint of segment
Point A has coordinates [15; 1] and the midpoint of the segment AB is the point [-20; 13]. What are the coordinates of point B?
Calculate the length of the segment AB, if the coordinates of the end vertices are A[-2, -4] and B[-5, -1].
Calculate distance between two points Z[7; -9] and U[-10; -8].
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.
- Angle between lines
Calculate the angle between these two lines: ? ?
If the endpoints of a diameter of a circle are A(10, -5) and B (8, 7), what is the radius of the circle?
Calculate the slope of a line that intersects points (38,-23) and (-93,5).
What is the slope of a line with an inclination 1.06 rad?
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