Problem 25 - College Algebra

Question

Find the midpoint of each line segment with the given endpoints. $$\left(-\frac{7}{2}, \frac{3}{2}\right) \text { and }\left(-\frac{5}{2},-\frac{11}{2}\right)$$

Step-by-Step Solution

Answer

The midpoint of the line segment is (-3, -2).

Step 1: Identify the Coordinates

First, identify the coordinates of the two endpoints given. Endpoint A is \(-\frac{7}{2}, \frac{3}{2}\) and endpoint B is \(-\frac{5}{2},-\frac{11}{2}\). So, \(x_1 = -\frac{7}{2}\), \(y_1 = \frac{3}{2}\), \(x_2 = -\frac{5}{2}\), and \(y_2 = -\frac{11}{2}\).

Step 2: Apply the midpoint formula

Next, substitute the identified coordinates into the midpoint formula. The midpoint, M is given by \(\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\) which translates to \(\left(\frac{ (-\frac{7}{2}) + (-\frac{5}{2}) }{2}, \frac{ (\frac{3}{2}) + (-\frac{11}{2}) }{2} \right)\).

Step 3: Calculate the midpoint

Now calculate the expressions in each of the brackets. The x-coordinate of the midpoint is \(\frac{-7 - 5}{4} = -3\) and the y-coordinate of the midpoint is \(\frac{3 - 11}{4} = -2\).