Two points are located at (−9, −8) and (−6, −4). Complete the equations below to show how you can use the Pythagorean theorem to find the distance between these two points.
Solve a² + b² = c² for c.
c =
Use coordinates to write an expression for the distance between the two points.
c = √(____ – ____)² + (____ – ____)²
To find the distance between the two points ((-9, -8)) and ((-6, -4)) using the Pythagorean theorem, we can follow these steps:
1. Identify the differences in the x and y coordinates:
– The difference in x-coordinates: (-6 – (-9) = -6 + 9 = 3)
– The difference in y-coordinates: (-4 – (-8) = -4 + 8 = 4)
2. Using the Pythagorean theorem:
The distance (c) can be found using the formula (c = sqrt{a^2 + b^2}). Here, (a) is the difference in x-coordinates, and (b) is the difference in y-coordinates.
3. Calculate (c):
[
c = sqrt{(3)^2 + (4)^2}
]
[
c = sqrt{9 + 16} = sqrt{25} = 5
]
So, we can express it as:
– (c = 5)
4. Distance formula using coordinates:
The expression for the distance between the two points using their coordinates would be:
[
c = sqrt{(-6 – (-9))^2 + (-4 – (-8))^2}