# Line - examples

1. Trapezium diagonals
It is given trapezium ABCD with bases | AB | = 12 cm, |CD| = 8 cm. Point S is the intersection of the diagonals for which |AS| is 6 cm long. Calculate the length of the full diagonal AC.
2. Angle between lines
Calculate the angle between these two lines: ? ?
3. Slope
What is the slope of a line with an inclination -221°?
4. 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
5. Hexagon - MO
The picture shows the ABCD square, the EFGD square and the HIJD rectangle. Points J and G lie on the side CD and is true |DJ|
6. XY triangle
Determine area of triangle given by line 7x+8y-69=0 and coordinate axes x and y.
7. Pizza master
Master says that he can splits pizza to 16 parts by five equals straight cuts. Is it possible?
8. Perpendicular
What is the slope of the perpendicular bisector of line segment AB if A[-4,-5] and B[1,-1]?
9. Lines
In how many points will intersect 14 different lines, where no two are parallel?
10. Perpendicular
Determine the slope of the line perpendicular to the line p: y = -x +4.
11. 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.
12. Center
In the triangle ABC is point D[1,-2,6], which is the center of the |BC| and point G[8,1,-3], which is the center of gravity of the triangle. Find the coordinates of the vertex A[x,y,z].
13. Cone
If the segment of the line y = -3x +4 that lies in quadrant I is rotated about the y-axis, a cone is formed. What is the volume of the cone?
14. Line
Line p passing through A[-10, 6] and has direction vector v=(3, 2). Is point B[7, 30] on the line p?
4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall?
16. Square side
Calculate length of side square ABCD with vertex A[0, 0] if diagonal BD lies on line p: -4x -5 =0.
17. The angle of lines
Calculate the angle of two lines y=x-21 and y=-2x+14
18. Angle
A straight line p given by the equation ?. Calculate the size of angle in degrees between line p and y-axis.
19. Circles
In the circle with a radius 7.5 cm are constructed two parallel chord whose lengths are 9 cm and 12 cm. Calculate the distance of these chords (if there are two possible solutions write both).
20. Circles
How many different circles is determined by 9 points at the plane, if 6 of them lie in a straight line?

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