Questions: Find the midpoint of the line segment joining points A and B. A(2,-5) ; B(4,1) The midpoint of the line segment is . (Type an ordered pair.)

Transcript text: Find the midpoint of the line segment joining points $A$ and $B$. \[ A(2,-5) ; B(4,1) \] The midpoint of the line segment is $\square$ . (Type an ordered pair.)

Solution

Solution Steps

To find the midpoint of a line segment joining two points $ A(x_1, y_1) $ and $ B(x_2, y_2) $, we use the midpoint formula: \[ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] Given points $ A(2, -5) $ and $ B(4, 1) $, we substitute these values into the formula to find the midpoint.

Step 1: Identify the Points

We are given two points $ A(2, -5) $ and $ B(4, 1) $.

Step 2: Apply the Midpoint Formula

To find the midpoint $ M $ of the line segment joining points $ A $ and $ B $, we use the midpoint formula: \[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] Substituting the coordinates of points $ A $ and $ B $: \[ M = \left( \frac{2 + 4}{2}, \frac{-5 + 1}{2} \right) \]

Step 3: Calculate the Midpoint

Calculating the x-coordinate: \[ \frac{2 + 4}{2} = \frac{6}{2} = 3.0 \] Calculating the y-coordinate: \[ \frac{-5 + 1}{2} = \frac{-4}{2} = -2.0 \] Thus, the midpoint $ M $ is $ (3.0, -2.0) $.