Find midpoint M of the line segment with endpoints A(-1.4, 2.5) and B (2.6, -1.5). Enter both responses as a decimal value to the tenth place.

1 answer

To find the midpoint \( M \) of the line segment with endpoints \( A(x_1, y_1) \) and \( B(x_2, y_2) \), we use the midpoint formula:

\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]

Given the points \( A(-1.4, 2.5) \) and \( B(2.6, -1.5) \), we can identify the coordinates as follows:

  • \( x_1 = -1.4 \)
  • \( y_1 = 2.5 \)
  • \( x_2 = 2.6 \)
  • \( y_2 = -1.5 \)

Now, we can calculate the x-coordinate of midpoint \( M \):

\[ x_M = \frac{-1.4 + 2.6}{2} = \frac{1.2}{2} = 0.6 \]

Next, we calculate the y-coordinate of midpoint \( M \):

\[ y_M = \frac{2.5 + (-1.5)}{2} = \frac{2.5 - 1.5}{2} = \frac{1.0}{2} = 0.5 \]

Thus, the coordinates of the midpoint \( M \) are:

\[ M(0.6, 0.5) \]

Finally, entering both responses as decimal values to the tenth place:

  • \( x \)-coordinate: \( 0.6 \)
  • \( y \)-coordinate: \( 0.5 \)

The answer is \( M(0.6, 0.5) \).