To find the distance \(d\) between two points \(A(x_1, y_1)\) and \(B(x_2, y_2)\), you can use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
In this case, the coordinates of the points \(A\) and \(B\) are given as \(A(-3, 4)\) and \(B(2, -3)\).
Let's identify the coordinates:
- \(x_1 = -3\), \(y_1 = 4\) (from point \(A\))
- \(x_2 = 2\), \(y_2 = -3\) (from point \(B\))
Now, applying the distance formula:
\[ d = \sqrt{(2 - (-3))^2 + (-3 - 4)^2} \] \[ = \sqrt{(2 + 3)^2 + (-3 - 4)^2} \] \[ = \sqrt{(5)^2 + (-7)^2} \] \[ = \sqrt{25 + 49} \] \[ = \sqrt{74} \]
Now, looking at the options you provided, let's find the one that correctly applies the distance formula:
A. \(d = \sqrt{(-4-3)^2 + (-3-2)^2}\) (incorrect)
B. \(d = \sqrt{(2 - (-3))^2 + (-3 - 4)^2}\) (correct)
C. \(d = \sqrt{(-3 - 4)^2 + (2 - (-3))^2}\) (incorrect)
D. \(d = \sqrt{(-4 + 3)^2 + (3 - (-2))^2}\) (incorrect)
Thus, the correct answer is B: \(d = \sqrt{(2 - (-3))^2 + (-3 - 4)^2}\).