Find the distance between the points \( (3, 4) \) and \( (7, 1) \) in the Cartesian plane.
Show Hint
- \( 5 \)
- \( \sqrt{50} \)
- \( \sqrt{41} \)
\( \sqrt{34} \)
The Correct Option is A
Solution and Explanation
The distance between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by the distance formula: \[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] For the points \( (3, 4) \) and \( (7, 1) \): \[ x_1 = 3, \ y_1 = 4, \ x_2 = 7, \ y_2 = 1 \] \[ \text{Distance} = \sqrt{(7 - 3)^2 + (1 - 4)^2} = \sqrt{4^2 + (-3)^2} = \sqrt{16 + 9} = \sqrt{25} = 5 \] Thus, the distance is: \[ {5} \]
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