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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 points ((-9, -8)) and ((-6, -4)), we can use the Pythagorean theorem.
1. First, we identify the horizontal and vertical distances between the points:
– The horizontal distance (change in x) is: (-6 – (-9) = -6 + 9 = 3)
– The vertical distance (change in y) is: (-4 – (-8) = -4 + 8 = 4)
2. Now, we can set up the Pythagorean theorem:
[
a^2 + b^2 = c^2
]
Here, (a = 3) (horizontal distance) and (b = 4) (vertical distance).
3. Plugging in the values:
[
c^2 = 3^2 + 4^2
]
[
c^2 = 9 + 16 = 25
]
[
c = sqrt{25} = 5
]
So, the equation to express the distance between the points is:
c = √( (3)² + (4)² )
The final answer for the distance (c) is 5. This demonstrates how we can use the Pythagorean theorem to calculate the distance between two points in a
To find the distance between the points ((-9, -8)) and ((-6, -4)), we can treat the difference in their coordinates as the two legs of a right triangle.
1. Find the lengths of the legs (a and b):
– The change in the x-coordinates (a) is:
[
-6 – (-9) = -6 + 9 = 3
]
– The change in the y-coordinates (b) is:
[
-4 – (-8) = -4 + 8 = 4
]
2. Apply the Pythagorean theorem:
[
a^2 + b^2 = c^2
]
Plugging in the values:
[
3^2 + 4^2 = c^2
]
Simplifying it:
[
9 + 16 = c^2
]
[
25 = c^2
]
Taking the square root of both sides:
[
c = 5
]
3. Write the distance formula using coordinates:
[
c = sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}
]
Substituting the