1. Prakash Adhikari Islington College, Kathmandu 1

2. Pure Mathematics (P1)- 9709 Topic: Co-ordinate Geometry 2

3. Lesson Description In this lesson, we will learn: Distance between two points of a line segment Mid point of the line segment joining two points Gradient (Slope) of the line segment – Gradient of Parallel lines – Gradient of Perpendicular lines 3

4. Compare with chart alongside.. 4 Y X A(x 1,y 1 ) x1x1 x2x2 y1y1 y2y2 B(x 2,y 2 )

5. Compare with chart alongside.. 5 Y X A(x 1,y 1 x1x1 x2x2 y1y1 y2y2 B(x 2,y 2 )

6. Compare with chart alongside.. 6 Y X A(x 1,y 1 ) x1x1 x2x2 y1y1 y2y2 B(x 2,y 2 ) d

7. Compare with chart alongside.. 7 Y X A(x 1,y 1 ) x1x1 x2x2 y1y1 y2y2 B(x 2,y 2 ) d

8. 8 Y X A(x 1,y 1 ) x1x1 x2x2 y1y1 y2y2 B(x 2,y 2 ) (y 2 -y 1 ) (x 2 -x 1 ) d

9. z 9 Y X A(x 1,y 1 ) x1x1 x2x2 y1y1 y2y2 B(x 2,y 2 ) (y 2 -y 1 ) (x 2 -x 1 ) d

10. 10 Y X A(x 1,y 1 ) x1x1 x2x2 y1y1 y2y2 B(x 2,y 2 ) (y 2 -y 1 ) (x 2 -x 1 ) d

11. Example: Distance between two points: A (9,7) and B(3,2) 11

12. 12 Y X A(x 1,y 1 ) x1x1 x2x2 y1y1 y2y2 B(x 2,y 2 )

13. 13 Y X A(x 1,y 1 ) x1x1 x2x2 y1y1 y2y2 B(x 2,y 2 )

14. 14 Y X A(x 1,y 1 ) x1x1 x2x2 y1y1 y2y2 B(x 2,y 2 ) C

15. 15 Y X A(x 1,y 1 ) x1x1 x2x2 y1y1 y2y2 B(x 2,y 2 ) C

16. 16

17. Slope of the line: 17 Definition of Slope The slope of the line through the distinct points (x 1, y 1 ) and (x 2, y 2 ) is Definition of Slope The slope of the line through the distinct points (x 1, y 1 ) and (x 2, y 2 ) is Change in y Change in x = Rise Run = y 2 – y 1 x 2 – x 1 (x 1, y 1 ) x1x1 y1y1 x2x2 y2y2 (x 2, y 2 ) Rise y 2 – y 1 Run x 2 – x 1 x y The steepness of a line, called the slope of the line. Slope compares the vertical change (the rise) to the horizontal change (the run) when moving from one fixed point to another along the line. A ratio comparing the change in y (the rise) with the change in x (the run) is used calculate the slope of a line.

18. Rise = 4 Run = 5

19. Sample Problems: Find the slope of the line thru the points given:  (-3,-1) and (-2,4)  (-3,4) and (2,-2)

20. The Possibilities for a Line’s Slope Positive Slope x y m > 0 Line rises from left to right. Zero Slope x y m = 0 Line is horizontal. m is undefined Undefined Slope x y Line is vertical. Negative Slope x y m < 0 Line falls from left to right.

21. Slope of second line m 2 Slope of First line m 1 Two lines are parallel if m 1= m 2

22. The End