Q2. Find the length of segment \( \overline{AB} \). Give exact value.

Background

Topic: Distance Formula in Coordinate Geometry

This question is testing your ability to calculate the length of a line segment between two points in the coordinate plane using the distance formula.

Key formula:

The distance between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by:

• \( x_1, y_1 \): Coordinates of point A

• \( x_2, y_2 \): Coordinates of point B

• \( D \): Length of the segment \( \overline{AB} \)

Step-by-Step Guidance

1. Identify the coordinates of points A and B from the diagram: \( A(-3, 4) \) and \( B(2, -3) \).

   

2. Write the distance formula:

3. Substitute the values:

4. Calculate the differences: and

5. Square the differences: and

Try solving on your own before revealing the answer!