1)Directed and Undirected Line Segments

*line segment -- made by joining two points called the endpoints. *directed line segments -- in what sense the line segment is measured; Sign Convention -->from left to right: positive; from right to left: negative; from bottom to top: positive; from top to bottom: negative. *undirected line segments -- always positive; also called the distance from one endpoint to another.

2)Rectangular Coordinates

*Rectangular Coordinates -- introduced by Rene Descartes; a point in space is represented by an ordered pair (x,y). *Rectangular coordinate system -- composed of two perpendicular lines drawn horizontally and vertically and are intersecting each other at a point called the origin. *x-axis -- the horizontal line. *y-axis -- the vertical line. *abscissa -- also called the x-coordinate; it is the distance of the point (x,y) from the y-axis. *ordinate -- also called the y-coordinate; it is the distance of the point (x,y) from the x-axis. *One-to-one correspondence -- each point on the rectangular coordinate system is represented by a unique real number and vice-versa.

3)Distance Between Two Points

*Distance Formula -- the distance from a point P1(x1, y1) to P2(x2,y2) is described by the formula:

4)Midpoint of a Line Segment

*Midpoint Formula -- the midpoint of a line segment with endpoints P1 (x1,y1) and P2 (x2,y2) is calculated using the following equations:

5)Division of a Line Segment

*Internal Division -- a line segment is divided such that the point of division P(x,y) is between the endpoints P1 (x1,y1) and P2 (x2,y2). *External Division -- a line segment is extended where the point of division is farther from the endpoints. Let the ratio of the directed distance from P1 to P and the directed distance from P to P2 be equal to the r1/r2. The equation to find the coordinates of P(x,y) are summarized below:

6)Inclination; Slope

*Angle of Inclination -- or simply the inclination is the minimum positive angle drawn from the positive x-axis to the line, the direction being counter-clockwise. *Slope -- defined as the tangent of the angle of inclination; also defined as rise over run. The slope of a line (m) containing P1 (x1,y1) and P2(x2,y2) is defined by:

7)Parallel and Perpendicular Lines

*Parallel Lines -- these lines have the same angle of inclination; they do not intersect each other; they have the same slopes. *Perpendicular Lines -- intersect each other at right angles or 90 degrees. Parallel and perpendicular lines have slopes which are negative reciprocals of each other. *Vertical Lines -- does not incline to the right nor to the left; they are parallel to the y-axis. By definition, vertical lines have no slope (no run) or undefined. *Horizontal lines -- parallel to the x-axis; slope is zero (no rise).

8)Angle Between Two Lines

*Angle between two lines -- is drawn from line 1 to line 2 in a counter-clockwise direction. If m1 is the slope of line 1 and m2 is the slope of line 2 and angle theta is the angle between the two lines, angle theta is solved by using the formula:

9)Area of a Triangle (given the vertices)

*Area of a triangle -- usually computed as (1/2)bh. Given the three points (P1, P2, P3) in a triangle called the vertices, its area can be solved using the formula:

It has to be noted that the three points must be in a counter-clockwise order as they are plotted. The formula above can be expanded to give: