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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 two points (-9, -8) and (-6, -4), we can use the Pythagorean theorem.
1. Identifying the changes in coordinates (Δx and Δy):
– Δx = x2 – x1 = -6 – (-9) = -6 + 9 = 3
– Δy = y2 – y1 = -4 – (-8) = -4 + 8 = 4
2. Using the Pythagorean theorem:
– We can say a² + b² = c² where:
– a = Δx = 3
– b = Δy = 4
3. Applying the values:
– c² = (3)² + (4)²
– c² = 9 + 16
– c² = 25
4. Solving for c:
– c = √(25) = 5
5. Writing the expression for distance using coordinates:
– c = √(−6 – (−9))² + (−4 – (−8))²
– c = √(3)² + (4)²
In summary:
– The distance between the two points is 5.
– The expression using the coordinates is **c = √(3)² + (4)²