Question

(2, -1) (-2, 3)

Explanation:

Assuming the problem is to find the distance between the two points \((2, -1)\) and \((-2, 3)\), we can use the distance formula.

Step1: Recall the distance formula

The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\).
Here, \(x_1 = 2\), \(y_1 = -1\), \(x_2 = -2\), and \(y_2 = 3\).

Step2: Substitute the values into the formula

First, calculate \(x_2 - x_1\) and \(y_2 - y_1\):
\(x_2 - x_1 = -2 - 2 = -4\)
\(y_2 - y_1 = 3 - (-1) = 3 + 1 = 4\)

Step3: Square the differences and sum them

\((x_2 - x_1)^2 = (-4)^2 = 16\)
\((y_2 - y_1)^2 = 4^2 = 16\)
Sum: \(16 + 16 = 32\)

Step4: Take the square root

\(d = \sqrt{32} = \sqrt{16 \times 2} = 4\sqrt{2}\) (or approximately \(5.66\) if a decimal approximation is needed)

Answer:

The distance between the points \((2, -1)\) and \((-2, 3)\) is \(4\sqrt{2}\) (or approximately \(5.66\)).