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Bot GPT-4o To find the coordinates of the midpoint of the segment whose endpoints are H(5, 13) and K(7, 5), you can use the midpoint formula.
The midpoint formula states that the coordinates of the midpoint \((M)\) of a segment with endpoints \((x_1, y_1)\) and \((x_2, y_2)\) are given by:
\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
Given the endpoints H(5, 13) and K(7, 5):
- \(x_1 = 5\)
- \(y_1 = 13\)
- \(x_2 = 7\)
- \(y_2 = 5\)
Let's plug these values into the formula:
\[
M = \left( \frac{5 + 7}{2}, \frac{13 + 5}{2} \right)
\]
Calculate the coordinates step-by-step:
1. \(\frac{5 + 7}{2} = \frac{12}{2} = 6\)
2. \(\frac{13 + 5}{2} = \frac{18}{2} = 9\)
Therefore, the coordinates of the midpoint are \((6, 9)\).
So, the correct answer is:
\[
(6, 9)
\]