The document provides instructions and examples for calculating the midpoint and distance between two points on a coordinate plane. It explains that to find the midpoint, you plot the two points, join them with a line, guess the middle point, then take the average of the x-coordinates and y-coordinates. To find the distance, you plot the points, form a right triangle, square the difference in x-coordinates and y-coordinates, add those values, and take the square root of the sum. It then works through examples of finding the midpoint of (4,3) to (6,1), and calculating distances between several pairs of points.

1. Mid point Rule Plot the points. Join the two points together. Guess where the middle is. Then Mid add and divide by 2 You should get the same answer as your guess

2. Open up book on page 304 Question 4 Find the midpoint of the line joining (4,3) to (6,1) First plot the points and join them

6. Rule mid add and divide by 2 +6 +1 +4 +3 +10 +4 Now divide each number by 2 Answer: The mid point is (5,2)

7. Next to find the distance between two points Rule Plot the points Join the points to form a line Make a right angled triangle Find the height of the triangle Find the length of the triangle Square, add and square root

8. Page 302 question 6 Find the distance (4,3) and (-2,5) First plot your points

13. Height = 2 length =6 Rule Square 2 x 2 = 4 6 x 6 = 36 Add 4 +36 = 40 √ 40

14. Answer Therefore the length of the line between (4,3) and (-2,5) is √ 40

16. Page 302 question 10 Find the distance between the points (-6,1) and (1,4 ) First write down the rule

17. Rule Plot the points Join the points Make a right angled triangle Find the height and length of the triangle Square, add and square root

19. Plot the points and join them

20. Make a right angled triangle

21. Find the height and length

23. Height = 3 Length = 7 Rule 1 Square 3 x3 =9 7 x 7 =49 2. Add 9 + 49 = 58 3 .Square Root √58

24. The length of the line is √58

25. Question 15 page 303 Find the distance between the points (-3,-2) and (5,-1) Write down the Rule

26. Rule Plot the points 1 Join the points to form a line 2 Make a right angled triangle 3 Find the height of the triangle 4 Find the length of the triangle 5 Square, add and square root

31. Height = 1 length = 8 Rule Squar e 1x1 =1 8x8 =64 Add 64 +1 =65 Square Root = √65

32. Answer: the Length of the line is √65