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.
- Quadrilateral 2
Show that the quadrilateral with vertices P1(0,1), P2(4,2) P3(3,6) P4(-5,4) has two right triangles.
- Vertices of RT
Show that the points P1 (5,0), P2 (2,1) & P3 (4,7) are the vertices of a right triangle.
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.
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: ?
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)?
Determine the slope of the line perpendicular to the line p: y = 9x +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?
- 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 length of the segment AB, if the coordinates of the end vertices are A[-2, -4] and B[-5, -1].
- 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 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?
What is the slope of a line with an inclination 1.06 rad?
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