To find the distance between point A \((-3, 5)\) and point B \((7, 2)\), we can use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Where:
- \((x_1, y_1) = (-3, 5)\) (Point A)
- \((x_2, y_2) = (7, 2)\) (Point B)
Substituting the values into the formula:
\[ d = \sqrt{(7 - (-3))^2 + (2 - 5)^2} \] \[ d = \sqrt{(7 + 3)^2 + (2 - 5)^2} \] \[ d = \sqrt{(10)^2 + (-3)^2} \] \[ d = \sqrt{100 + 9} \] \[ d = \sqrt{109} \] \[ d \approx 10.4403 \]
Rounding to the nearest tenth, the distance from point A to point B is approximately 10.4 units.
To find the midpoint of line segment AB, we can use the midpoint formula:
\[ \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
Substituting the coordinates of points A and B:
\[ \text{Midpoint} = \left( \frac{-3 + 7}{2}, \frac{5 + 2}{2} \right) \] \[ \text{Midpoint} = \left( \frac{4}{2}, \frac{7}{2} \right) \] \[ \text{Midpoint} = \left( 2, 3.5 \right) \]
Thus, the midpoint of line segment AB is (2, 3.5).
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