To find the distance 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 your case, the coordinates for the points are:
- \( A(-3, 4) \) with \( x_1 = -3 \) and \( y_1 = 4 \)
- \( B(2, -3) \) with \( x_2 = 2 \) and \( y_2 = -3 \)
Now, plug in the values into the distance formula:
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Calculate \( x_2 - x_1 \): \[ x_2 - x_1 = 2 - (-3) = 2 + 3 = 5 \]
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Calculate \( y_2 - y_1 \): \[ y_2 - y_1 = -3 - 4 = -7 \]
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Substitute these results into the distance formula: \[ d = \sqrt{(5)^2 + (-7)^2} \] \[ = \sqrt{25 + 49} \] \[ = \sqrt{74} \]
Thus, the distance between points \( A \) and \( B \) is \( \sqrt{74} \). If you need the numerical approximation, it is approximately \( 8.60 \).