To find the distance between two points in a Cartesian coordinate system, you can use the distance formula. Let’s say you have two points: \( P(x_1, y_1) \) and \( Q(x_2, y_2) \).
The distance \( d \) between these two points is given by the formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Steps to Calculate Distance:
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Identify the Coordinates: Determine the coordinates of the two points you're interested in.
- For example, if \( P(3, 4) \) and \( Q(7, 1) \), then \( x_1 = 3, y_1 = 4, x_2 = 7, y_2 = 1 \).
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Substitute the Values into the Formula: \[ d = \sqrt{(7 - 3)^2 + (1 - 4)^2} \]
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Calculate the Differences:
- \( x_2 - x_1 = 7 - 3 = 4 \)
- \( y_2 - y_1 = 1 - 4 = -3 \)
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Square the Differences:
- \( (4)^2 = 16 \)
- \( (-3)^2 = 9 \)
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Sum the Squares: \[ d = \sqrt{16 + 9} = \sqrt{25} \]
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Find the Square Root: \[ d = 5 \]
Conclusion:
The distance between the points \( P(3, 4) \) and \( Q(7, 1) \) is 5 units.
If you have specific points in mind, feel free to share them, and I can demonstrate the calculation using those coordinates!