# Analytic geometry - high school - math problems

Also known as coordinate geometry or Cartesian geometry.

1. Distance between 2 points Find the distance between the points (7, -9), (-1, -9)
2. Find the 10 Find the value of t if 2tx+5y-6=0 and 5x-4y+8=0 are perpendicular, parallel, what angle does each of the lines make with the x-axis, find the angle between the lines?
3. Touch x-axis Find the equations of circles that pass through points A (-2; 4) and B (0; 2) and touch the x-axis.
4. Coordinates of square vertices The ABCD square has the center S [−3, −2] and the vertex A [1, −3]. Find the coordinates of the other vertices of the square.
5. Coordinates of square vertices I have coordinates of square vertices A / -3; 1/and B/1; 4 /. Find coordinates of vertices C and D, C 'and D'. Thanks Peter.
6. Three points Three points A (-3;-5) B (9;-10) and C (2;k) . AB=AC What is value of k?
7. Distance problem A=(x, x) B=(1,4) Distance AB=√5, find x;
8. Distance problem 2 A=(x,2x) B=(2x,1) Distance AB=√2, find value of x
9. Set of coordinates Consider the following ordered pairs that represent a relation. {(–4, –7), (0, 6), (5, –3), (5, 2)} What can be concluded of the domain and range for this relation?
10. 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 square units. The segment passes through the point ( 5,2). What is the slope of the line segment?
11. A screen A screen is 1680 x 1050 pixels. What are the coordinates (and size in pixels) of an centered area which is exactly 33% of the screen size?
12. Coordinates of vector Determine the coordinate of a vector u=CD if C(19;-7) and D(-16;-5)
13. Find parameters Find parameters of the circle in the plane - coordinates of center and radius: ?
14. Ellipse Ellipse is expressed by equation 9x2 + 25y2 - 54x - 100y - 44 = 0. Find the length of primary and secondary axes, eccentricity, and coordinates of the center of the ellipse.
15. Hyperbola Find the equation of hyperbola that passes through the point M [30; 24] and has focal points at F1 [0; 4 sqrt 6], F2 [0; -4 sqrt 6].
16. Prove 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
17. Two people Two straight lines cross at right angles. Two people start simultaneously at the point of intersection. John walking at the rate of 4 kph in one road, Jenelyn walking at the rate of 8 kph on the other road. How long will it take for them to be 20√5 km apar
18. Vertices of a right triangle Show that the points D(2,1), E(4,0), F(5,7) are vertices of a right triangle.
19. Sphere equation Obtain the equation of sphere its centre on the line 3x+2z=0=4x-5y and passes through the points (0,-2,-4) and (2,-1,1).
20. Symmetry by plane Determine the coordinates of a image of point A (3, -4, -6) at a symmetry that is determined by the plane x-y-4z-13 = 0

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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.