# Analytic geometry - examples

Also known as coordinate geometry or Cartesian geometry.- Three points

Three points A (-3;-5) B (9;-10) and C (2;k) . AB=AC What is value of k? - On line

On line p: x = 4 + t, y = 3 + 2t, t is R, find point C, which has the same distance from points A [1,2] and B [-1,0]. - Center of line segment

Calculate the distance of the point X [1,3] from the center of the line segment x = 2-6t, y = 1-4t ; t is . - Coordinates of vector

Determine the coordinate of a vector u=CD if C(19;-7) and D(-16;-5) - Distance problem 2

A=(x,2x) B=(2x,1) Distance AB=√2, find value of x - Distance problem

A=(x, x) B=(1,4) Distance AB=√5, find x; - Forces

In point O acts three orthogonal forces: F_{1}= 20 N, F_{2}= 7 N and F_{3}= 19 N. Determine the resultant of F and the angles between F and forces F_{1}, F_{2}and F_{3}. - Triangle

Triangle KLM is given by plane coordinates of vertices: K[-12, -11] L[-15, -18] M[-13, -12]. Calculate its area and itsinterior angles. - Speed of Slovakian trains

Rudolf decided to take the train from the station 'Trnava' to 'Zemianske Kostoľany'. In the train timetables found train R 725 Remata : km0Bratislava hl.st.12:574Bratislava-Vinohrady13:0113:0219Pezinok13:1213:1346Trnava13:3013:3263Leopoldov13:4514:0168H - Center

Calculate the coordinates of the center of gravity T [x, y] of triangle ABC; A[11,4] B[13,-7] C[-17,-18]. - Angle between lines

Calculate the angle between these two lines: ? ? - Angle between vectors

Find the angle between the given vectors to the nearest tenth of a degree. u = (-22, 11) and v = (16, 20) - Slope

What is the slope of a line with an inclination -221°? - Circle

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-10 = 0 q: -x-19 = 0 a: 9x-4y+5 = 0 - XY triangle

Determine area of triangle given by line 7x+8y-69=0 and coordinate axes x and y. - 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. - Circle

Write the equation of a circle that passes through the point [0,6] and touch the X-axis point [5,0]: ? - Distance

Calculate distance between two points X[18; 19] and W[20; 3]. - Perpendicular

What is the slope of the perpendicular bisector of line segment AB if A[-4,-5] and B[1,-1]? - Perpendicular

Determine the slope of the line perpendicular to the line p: y = -x +4.

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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. See also more information on Wikipedia.