Question

What is the distance between the points $(3, -2)$ and $(-1, 4)$?

• A. 6
• B. \(\frac{5}{2}\)
• C. \(\sqrt{52}\)
• D. 8

Hint:

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

Answer 1

The Correct Option is C

The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Here, the coordinates are \((x_1, y_1) = (3, -2)\) and \((x_2, y_2) = (-1, 4)\). Substitute the values: \[ d = \sqrt{(-1 - 3)^2 + (4 - (-2))^2} = \sqrt{(-4)^2 + (6)^2} = \sqrt{16 + 36} = \sqrt{52} \] So, the distance between the points is \(\sqrt{52}\).
Final answer
Answer: \(\boxed{\sqrt{52}}\)