2. OBJECTIVES : At the end of the lesson, the student is expected to be able to: • Familiarize with the use of Cartesian Coordinate System. • Determine the distance between two points. • Determine the area of a polygon by coordinates.
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5. Directed Line – a line in which one direction is chosen as positive and the opposite direction as negative. Directed Line Segment – consisting of any two points and the part between them. Directed Distance – the distance between two points either positive or negative depending upon the direction of the line. DEFINITION :
6. RECTANGULAR COORDINATES A pair of number (x, y) in which x is the first and y being the second number is called an ordered pair . A vertical line and a horizontal line meeting at an origin, O, are drawn which determines the coordinate axes .
7. Coordinate Plane – is a plane determined by the coordinate axes. P (x, y) o y x
8. x – axis – is usually drawn horizontally and is called as the horizontal axis. y – axis – is drawn vertically and is called as the vertical axis. o – the origin coordinate – a number corresponds to a point in the axis, which is defined in terms of the perpendicular distance from the axes to the point. abscissa – is the x-coordinate of an ordered pair. ordinate – is the y-coordinate of an ordered pair.
9. DISTANCE BETWEEN TWO POINTS The length of a horizontal line segment is the abscissa (x-coordinate) of the point on the right minus the abscissa (x-coordinate) of the point on the left. 1. Horizontal
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13. 3. Slant To determine the distance between two points of a slant line segment add the square of the difference of the abscissa to the square of the difference of the ordinates and take the positive square root of the sum.
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17. AREA OF A POLYGON BY COORDINATES Consider the triangle whose vertices are P 1 (x 1 , y 1 ), P 2 (x 2 , y 2 ) and P 3 (x 3 , y 3 ) as shown below. o y x
18. Then the area of the triangle is determined by: [in counterclockwise rotation] Generalized formula for the area of polygon by coordinates:
