Exercises for Seminar 2 (Line on plane)

Date: 2015-10-07; view: 432.

2.1. Compose an equation of the line passing through the point and is parallel to the following line: a) b) c) .

2.2. Compose an equation of the line passing through two points: a) and ;

b) and .

2.3. Determine whether the following lines are intersected, parallel or coincide; if lines are intersected, find the coordinates of the point of their intersection:

a) and ; b) and .

2.4. For which the lines and :

a) are intersected; b) are parallel; c) coincide?

2.5. A point is on line ; vector has the coordinates Prove that the point is in positive half-plane regarding to the line with an equation .

2.6. A point is the center of a parallelogram, and its sides lie on some four lines. On each of these lines one of the following points is located: . Find equations of the lines.

2.7. Compose an equation of the line passing through the point and is perpendicular to the following line: a) b) .

2.8. Find the distance from the point to the line given by its equation:

a) ; b) ; c) .

2.9. A point is on the line . The distance from the point to line is equal to 2. Find the coordinates of .

2.10. Find an angle between lines: a) and ;

b) and ; c) and .