Analytic geometry - examples
- Right triangle from axes
A line segment has its ends on the coordinate axes and forms with them a triangle of area equal to 36 sq. Units . The segment passes through the point ( 5,2). What is the slope of the line segment. ?
- Points collinear
Show that the point A(-1,3), B(3,2), C(11,0) are col-linear.
Prove that k1 and k2 is the equations of two circles. Find the equation of the line that passes through the centers of these circles. k1: x2+y2+2x+4y+1=0 k2: x2+y2-8x+6y+9=0
In point O acts three orthogonal forces: F1 = 20 N, F2 = 7 N and F3 = 19 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[-4, -18] L[-13, 15] M[-1, 8]. 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
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: ? ?
What is the slope of a line with an inclination -221°?
- Angle between vectors
Find the angle between the given vectors to the nearest tenth of a degree. u = (-22, 11) and v = (16, 20)
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.
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 [0,6] and touch the X-axis point [5,0]: ?
Calculate distance between two points X[18; 19] and W[20; 3].
What is the slope of the perpendicular bisector of line segment AB if A[-4,-5] and B[1,-1]?
Determine the slope of the line perpendicular to the line p: y = -x +4.
Circle is given by centre on S[-7; 10] and maximum chord 13 long. How many intersect points have circle with the coordinate axes?
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.
Calculate the coordinates of the circle center: ?
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.