Question

Find the length of a line segment joining the points \( A(2, -2) \) and \( B(3, 7) \).

Hint:

To find the distance between two points, use the distance formula \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).

Answer 1

The formula for the distance between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}. \] Here, the coordinates of \( A \) are \( (2, -2) \) and the coordinates of \( B \) are \( (3, 7) \). Substitute the values of \( x_1 = 2 \), \( y_1 = -2 \), \( x_2 = 3 \), and \( y_2 = 7 \) into the formula: \[ d = \sqrt{(3 - 2)^2 + (7 - (-2))^2} = \sqrt{1^2 + (7 + 2)^2} = \sqrt{1 + 9^2} = \sqrt{1 + 81} = \sqrt{82}. \] Thus, the length of the line segment is: \[ d = \sqrt{82} \approx 9.05 \text{ units}. \]