Pregunta
\( J(13,20) \) and \( K(-20,-14) \) are the endpoints of a line segment. What is the midpoint \( M \) of that line segment? Write the coordinates as decimals or integers. \( M=(\square) \)
Ask by Gardner Black. in the United States
Jan 23,2025
Solución de tutoría real
Respuesta verificada por el tutor
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The midpoint \( M \) is at \( (-3.5, \, 3) \).
Solución
To find the midpoint \( M \) of the line segment with endpoints \( J(13, 20) \) and \( K(-20, -14) \), we use the midpoint formula:
\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
Plugging in the coordinates:
\[
M_x = \frac{13 + (-20)}{2} = \frac{-7}{2} = -3.5
\]
\[
M_y = \frac{20 + (-14)}{2} = \frac{6}{2} = 3
\]
So, the midpoint \( M \) is:
\[
M = (-3.5, \, 3)
\]
**Answer:** \( M = (-3.5,\ 3) \)
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución Beyond the Answer
To find the midpoint \( M \) of the line segment with endpoints \( J(13,20) \) and \( K(-20,-14) \), you can use the midpoint formula: \[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] Plugging in the values: \[ M = \left( \frac{13 + (-20)}{2}, \frac{20 + (-14)}{2} \right) = \left( \frac{-7}{2}, \frac{6}{2} \right) = \left( -3.5, 3 \right) \] So, the coordinates of the midpoint \( M \) are \( M=(-3.5, 3) \).
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