Math

LESSON ONE: Fundamental Concepts

Problem Set 2

ANGLE BETWEEN TWO INTERSECTING LINES

1. Find the angle from the line through (-1, 6) and (5, -2) to the line through (4, -4) and (1, 7).

2. The angle from the line through (x, -1) and (-3, -5) to the line through (2, -5) and (4, 1) is 45. Find x.

3. Find the interior angles of the triangle A(5, 4), B(-1, 1) and C(3, -2).

4. A line through (-2, y) and (2, -10) is perpendicular to a line through (-3, -7) and (5, -5). Find y.

5. The line through the points (4, 3) and (-6, 0) intersects the line through (0, 0) and (-1, 5). Find the acute angle.

6. Two lines passing through (2, 3) make an angle of 45. If the slope of one of the lines is 2, find the slope of the other.

7. A line passing through (4, 7) makes an angle of 45 with the y-axis. Find the point where the line crosses the y-axis.

DIVISION OF A LINE SEGMENT

1. The line segment joining (-5, -3) and (3, 4) is to be divided into five equal parts. Find the point of division closest to (-5, -3).

2. Find the midpoint of the segment joining (7, -2) and (-3, 5).

3. The line segment from (1, 4) to (2, 1) is extended a distance equal to twice its length. Find terminal point.

4. On the line joining (4, -5) to (-4, -2), find the point which is three-seventh the distance from the first to the second point.

5. Find the trisection points of the line joining (-6, 2) and (3, 8).

6. A triangle with vertices A(4, -4), B(10, 4) and C(2, 6), find the point on each median that is two-thirds of the distance from the vertex to the midpoint of the opposite side.

7. What are the lengths of the segments into which the y-axis divides the segment joining (-6, -6) and (3, 6)?

8. Find the points which trisect the segment joining (9, 2) and (-3, 5).

9. A line passes through A(1, 1), B(4, 3). Find the coordinates of the point on the line which is (1) three times as far from A as from B, (2) three...