Question 2 Find the midpoint of the line segment from \( (-4,-2) \) to \( (2,2) \) Midpoint \( = \) Question Help: \( \square \) Video \( \square \) Message instructor Submit Question Jump to Answer

To find the midpoint of a line segment defined by two points, you can use the midpoint formula: \[ \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] In your case, plug in the values: \( (-4, -2) \) and \( (2, 2) \). This gives: \[ \text{Midpoint} = \left( \frac{-4 + 2}{2}, \frac{-2 + 2}{2} \right) = \left( \frac{-2}{2}, \frac{0}{2} \right) = (-1, 0) \] So, the midpoint is \( (-1, 0) \). Finding midpoints isn't just an academic exercise! This concept is widely used in fields like architecture when determining the best placement for structures, or in navigation systems to find optimal stopping points. Midpoints help ensure designs are balanced and anchor points are accurately identified. A common mistake when calculating midpoints is forgetting to average both the x and y coordinates separately. Always remember to handle each coordinate independently. Also, double-check arithmetic errors, especially when negatives and positives are involved – one small mistake can lead to an entirely different point!