1. Chapter 3 Section 3.1: Rectangular Coordinate System Objectives: Define the distance between two points Find the midpoint of a line segment United Arab Emirates University University General Requirement Unit

2. 3.1 Rectangular and Coordinate Planes x y x-axis y-axis Quadrant IQuadrant II Quadrant III Quadrant IV (0,0) + + + + + + + + + + + + + + --3 –2 –1 1 2 3 Each point P in an xy-plane can be assigned by an ordered pair (a,b) a = x-coordinate or abscissa, b = y-coordinate or ordinate. We write P(a,b) + + + + + + + + Chapter 3

3. Plotting Points on xy-plane (3,2) (0,3) (-4,3) (-6,0) (-4,-2) (0,-2) (4,-3) (0,0) (6,0)

4. Important notes Points on x-axis: Each point on x-axis has a y-coordinate zero. i.e, it is written in the form ( x, 0 ) Points on y-axis: Each point on y-axis has a x-coordinate zero. i.e, it is written in the form ( 0, y ) Sign of coordinates of points x-coordinate IV III II I y-coordinateQuadrant

5. Distance Between Two Points x y x1x1 x2x2 y 1 y 2 A(x 1,y 1 ) B(x 2,y 2 ) d d =

6. Example 1 Find the distance between the two points A ( 2, -3 ) and B ( 4, 5 ). Solution: D = = = = = =

7. Midpoint Formula x y x1x1 x2x2 y 1 y 2 A(x 1,y 1 ) B(x 2,y 2 ) x y M(x,y) Midpoint M(x,y) =

8. Example 2 Find the midpoint of P(3,2) and Q(-3,5). Solution: Let M be the midpoint of P and Q. Then M(x,y) = =

9. Homework Do all the homework assigned in the syllabus