Problem 24 - College Algebra

Question

Find the midpoint of each line segment with the given endpoints. $$(-2,-1) \text { and }(-8,6)$$

Step-by-Step Solution

Answer

The midpoint of the line segment with endpoints (-2, -1) and (-8, 6) is (-5, 2.5).

Step 1: Identify the Coordiantes

Identify the given coordinates. Here, we have \((x_1, y_1) = (-2, -1)\) and \((x_2, y_2) = (-8, 6)\).

Step 2: Substitute into Midpoint Formula

Next, substitute these coordinates into the midpoint formula: \(M = \left(\frac{x1+x2}{2}, \frac{y1+y2}{2}\right)\), giving \(M = \left(\frac{-2 + -8}{2}, \frac{-1 + 6}{2}\right)\).

Step 3: Compute the Midpoint

Compute the midpoint by adding and then dividing by two for each component (x and y). This gives \(M = \left(\frac{-10}{2}, \frac{5}{2}\right)\),thus the midpoint M is \(-5, 2.5\).