# 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

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. - Vector

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. - Center

Calculate the coordinates of the center of gravity T [x, y] of triangle ABC; A[27,-11] B[2,-30] C[11,12]. - Center

Calculate the coordinates of the circle center: ? - Circle

From the equation of a circle: ? Calculate the coordinates of the center of the circle S[x_{0}, y_{0}] and radius of the circle r. - Distance

Wha is the distance between the origin and the point (23; -7)? - Perpendicular

Determine the slope of the line perpendicular to the line p: y = 9x +7. - Circle

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) - Segment

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? - Distance

Calculate distance between two points Z[7; -9] and U[-10; -8]. - Line

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: ? ? - Diameter

If the endpoints of a diameter of a circle are A(10, -5) and B (8, 7), what is the radius of the circle? - Slope

What is the slope of a line with an inclination 1.06 rad?

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