To find the distance between the points \( (0, 6) \) and \( (-3, -2) \) using the Pythagorean Theorem, we can utilize the distance formula, which is derived from the theorem. The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Now, substituting the coordinates of the points \( (0, 6) \) and \( (-3, -2) \):
- \( x_1 = 0, y_1 = 6 \)
- \( x_2 = -3, y_2 = -2 \)
Substituting these values into the distance formula:
\[ d = \sqrt{((-3) - 0)^2 + ((-2) - 6)^2} \]
Calculating the differences:
\[ d = \sqrt{(-3)^2 + (-8)^2} \]
Calculating the squares:
\[ d = \sqrt{9 + 64} \]
Adding the squares:
\[ d = \sqrt{73} \]
Now, to find the numerical value of \( \sqrt{73} \):
\[ d \approx 8.54 \]
Thus, the distance between the points \( (0, 6) \) and \( (-3, -2) \) is approximately \( 8.54 \). Therefore, rounding it to the nearest hundredth, the answer is:
8.54
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