Bot GPT 4-o mini To find the length between the two points (3,2) and (7,8) using the Pythagorean Theorem, we can first determine the difference in the x-coordinates and the difference in the y-coordinates.
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Calculate the differences:
- Difference in x-coordinates: \( x_2 - x_1 = 7 - 3 = 4 \)
- Difference in y-coordinates: \( y_2 - y_1 = 8 - 2 = 6 \)
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Apply the Pythagorean Theorem:
The formula for the distance \( d \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Substituting the differences we calculated: \[ d = \sqrt{(4)^2 + (6)^2} \] \[ d = \sqrt{16 + 36} \] \[ d = \sqrt{52} \] \[ d \approx 7.21 \]
So, the length between the two points (3,2) and (7,8) is approximately 7.21, rounded to the nearest hundredth.
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