A line segment has the endpoints Q(–2.3, 9.3) and R(17.4, –5.2). Find the coordinates of its midpoint M.

Write the coordinates as decimals or integers.

1 answer

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

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

Given the points \( Q(-2.3, 9.3) \) and \( R(17.4, -5.2) \), we can identify:

  • \( x_1 = -2.3 \)
  • \( y_1 = 9.3 \)
  • \( x_2 = 17.4 \)
  • \( y_2 = -5.2 \)

Now we can plug the values into the midpoint formula:

  1. For the x-coordinate of the midpoint:

\[ \frac{x_1 + x_2}{2} = \frac{-2.3 + 17.4}{2} = \frac{15.1}{2} = 7.55 \]

  1. For the y-coordinate of the midpoint:

\[ \frac{y_1 + y_2}{2} = \frac{9.3 + (-5.2)}{2} = \frac{9.3 - 5.2}{2} = \frac{4.1}{2} = 2.05 \]

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

\[ M(7.55, 2.05) \]