6.1+Revisiting+Slopes

AD: November 11, 2008 (Day 29)
Big Idea: The dimensions of a right triangle can be determined with only limited information. Essential Question: What's 'irrational' about irrational numbers?

Problem 6.1
If Oskar had enough power, he could use a laser shield to walk right through the trees. Give the slope of the straight line path he could follow to get from point O to each of the labeled trees.**
 * The diagram below shows part of the forest. Some of the laser trees have been labeled with letters, and x and y axes have been added. Oskars location is labeled with an O.

Path to tree K: Oskar would have to go up 7and go over 1. Therefore change in y = 7 change in x = 1 Slope = change in y/change in x, therefore the slope of the required path would be 7/1

Path to tree J: Oskar would have to go up 7 and go over 2. Therefore change in y = 7 change in x = 2 Slope = change in y/change in x, therefore the slope of the required path would be 7/2

Path to tree I: Oskar would have to go up and go over. Therefore change in y = 7 change in x = 3 Slope = change in y/change in x, therefore the slope of the required path would be 7/3

Path to tree H: Oskar would have to go up 7 and go over 4. Therefore change in y = 7 change in x = 4 Slope = change in y/change in x, therefore the slope of the required path would be 7/4

Path to tree G: Oskar would have to go up 6 and go over 5. Therefore change in y = 6 change in x = 5 Slope = change in y/change in x, therefore the slope of the required path would be 6/5 Path to tree F: Oskar would have to go up 5 and go over 6. Therefore change in y = 5 change in x = 6 Slope = change in y/change in x, therefore the slope of the required path would be 5/6

Path to tree E: Oskar would have to go up 4 and go over 7. Therefore change in y = 4 change in x = 7 Slope = change in y/change in x, therefore the slope of the required path would be 4/7

Path to tree D: Oskar would have to go up 3 and go over 7. Therefore change in y = 3 change in x = 7 Slope = change in y/change in x, therefore the slope of the required path would be 3/7

Path to tree C:Oskar would have to go up 2 and go over 7. Therefore change in y = 2 change in x = 7 Slope = change in y/change in x, therefore the slope of the required path would be 2/7

Path to tree B: Oskar would have to go up 1 and go over 7. Therefore change in y = 1 change in x = 7 Slope = change in y/change in x, therefore the slope of the required path would be 1/7

Path to tree A: Oskar would have to go up 0 and go over 7. Therefore change in y = 0 change in x = 7 Slope = change in y/change in x, therefore the slope of the required path would be 0/7


 * __Follow Up__

1. Suppose the forest continues for a great distance in all directions. (a)** **Give the coordinates of two more trees on line OC. (b) Give the coordinates of two more trees on line OF.**

(a) To find the coordinates of the next 2 trees, i would have to multiply the coordinates (7,1) by 2 and 3. 7 X 2 = 14, 1 X 2 = 2 Therefore coordinates of the 1st tree: (14,2) 7 X 3 = 21, 1 X 3 = 3 Therefore the coordinates of the second tree: (21,3)

To find the coordinates of the next 2 trees, i would have to multiply the coordinates (6,5) by 2 and 3. 6 X 2 = 12, 5 X 2 = 10 Therefore coordinates of the 1st tree: (12,10) 6 X 3 = 18, 5 X 3 = 15 Therefore the coordinates of the 2nd tree: (18,15)

(b) What angle does the line described in part a make with the x-axis?**
 * 2. (a) Give the coordinates of three tress on the line with slope 1 that passes through point O

(a) The coordinates of three trees that would fall on the line are (1,1), (2,2), and (3,3) (b) The line makes an angle of 45 degrees with the x-axis.


 * 3. If a line contains two points on the grid, how can you find its slope?**

As described in the notes section, the formula for calculating the slope of a line is y1-y2/x1-x2, or more simply rise / run.


 * 4. If a line contains two points on a grid, will its slope be a rational number or an irrational number?**

If a line has two points on a grid, then we can calculate its slope using the formula given in question 4. This means that the slope of the line can be expressed as a fraction, which makes it a rational number. Therefore, the slope of a line with two points on a grid would always be a rational number.