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

Question

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

Quizzma Team · Answer

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

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