Arrange the pairs of points in increasing order of the slopes of the lines joining them.
To find the slopes of lines joining pairs of points, we can use the formula:
slope = (y2 - y1) / (x2 - x1)
Here are the steps to arrange the pairs of points in increasing order of slopes:
1. Start with the first pair of points and calculate the slope of the line joining them.
2. Move to the next pair of points and calculate the slope of the line joining them.
3. Compare the slopes of the two lines. If the slope of the second line is greater than the first, swap the positions of the two pairs of points.
4. Repeat this process for all pairs of points, comparing and swapping as necessary, until you reach the end.
5. Once you have compared and swapped all the pairs, you will have the pairs of points arranged in increasing order of the slopes of the lines joining them.
Here's an example to illustrate the process:
Let's say we have the following pairs of points:
A (2, 4)
B (5, 7)
C (1, 3)
D (3, 9)
1. Calculate the slopes:
Slope AB = (7 - 4) / (5 - 2) = 3/3 = 1
Slope AC = (3 - 4) / (1 - 2) = -1/-1 = 1
Slope AD = (9 - 4) / (3 - 2) = 5/1 = 5
2. Compare and swap:
Since the slope of AD (5) is greater than the slope of AB (1), swap the positions of AD and AB:
A (3, 9)
B (2, 4)
C (1, 3)
D (5, 7)
3. Repeat:
Now compare the slopes of AC and AB. They are the same (1), so no swap is needed.
Similarly, the slope of AC (1) is less than the slope of AD (5), so no further swaps are needed.
4. Final arrangement in increasing order of slopes:
C (1, 3)
A (2, 4)
B (3, 9)
D (5, 7)
Thus, the pairs of points are arranged in increasing order of the slopes of the lines joining them.