Question

Find the distance between the points \( (3, 4) \) and \( (7, 1) \) in the Cartesian plane.

• A. \( 5 \)
• B. \( \sqrt{50} \)
• C. \( \sqrt{41} \)
• D. \( \sqrt{34} \)

Hint:

Use the distance formula \( \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \) to find the distance between two points in the Cartesian plane.

Answer 1

The Correct Option is A

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: \[ {5} \]