To find the length between two points \( A(7, 8) \) and \( B(3, 2) \) in a 2D coordinate system, we can use the distance formula derived from the Pythagorean Theorem:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, \( (x_1, y_1) \) are the coordinates of point A, and \( (x_2, y_2) \) are the coordinates of point B. So, we have:
- \( x_1 = 7 \)
- \( y_1 = 8 \)
- \( x_2 = 3 \)
- \( y_2 = 2 \)
Now, substitute these values into the distance formula:
\[ d = \sqrt{(3 - 7)^2 + (2 - 8)^2} \]
Calculating the differences:
\[ d = \sqrt{(-4)^2 + (-6)^2} \]
Calculating the squares:
\[ d = \sqrt{16 + 36} \]
Adding:
\[ d = \sqrt{52} \]
To round that to the nearest hundredth, we first calculate \( \sqrt{52} \):
\[ \sqrt{52} \approx 7.2111 \]
Rounding to the nearest hundredth:
\[ d \approx 7.21 \]
Thus, the length between the two points A and B is approximately 7.21.