Line - 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.
- Two chords
There is a given circle k (center S, radius r). From point A which lies on circle k are starting two chords of length r. What angle does chords make? Draw and measure.
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
- Angle between lines
Calculate the angle between these two lines: ? ?
What is the slope of a line with an inclination -221°?
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
- 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|
- XY triangle
Determine area of triangle given by line 7x+8y-69=0 and coordinate axes x and y.
- Pizza master
Master says that he can splits pizza to 16 parts by five equals straight cuts. Is it possible?
What is the slope of the perpendicular bisector of line segment AB if A[-4,-5] and B[1,-1]?
In how many points will intersect 14 different lines, where no two are parallel?
Determine the slope of the line perpendicular to the line p: y = -x +4.
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.
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?
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].
Line p passing through A[-10, 6] and has direction vector v=(3, 2). Is point B[7, 30] on the line p?
- Square side
Calculate length of side square ABCD with vertex A[0, 0] if diagonal BD lies on line p: -4x -5 =0.
4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall?
- The angle of lines
Calculate the angle of two lines y=x-21 and y=-2x+14