Pregunta
\( A \) is the point \( (5,7) \) and \( B \) is the point \( (-1,-5) \). Find the coordinates of the mid-point of the line segment \( A B \). (2 marks)
Ask by Washington Nunez. in Singapore
Jan 24,2025
Solución de tutoría real
Respuesta verificada por el tutor
Responder
The midpoint of \( AB \) is \( (2,\ 1) \).
Solución
To find the midpoint \( M \) of the line segment \( AB \), use the midpoint formula:
\[
M = \left( \frac{x_A + x_B}{2}, \frac{y_A + y_B}{2} \right)
\]
Given:
- Point \( A = (5, 7) \)
- Point \( B = (-1, -5) \)
Plugging in the values:
\[
M = \left( \frac{5 + (-1)}{2}, \frac{7 + (-5)}{2} \right) = \left( \frac{4}{2}, \frac{2}{2} \right) = (2, 1)
\]
**Answer:** The midpoint of \( AB \) is \( (2,\ 1) \).
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Simplifique esta solución Mind Expander
To find the coordinates of the mid-point of the line segment connecting points \( A(5,7) \) and \( B(-1,-5) \), you can use the mid-point formula: \[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] Plugging in the coordinates of points \( A \) and \( B \): \[ M = \left( \frac{5 + (-1)}{2}, \frac{7 + (-5)}{2} \right) = \left( \frac{4}{2}, \frac{2}{2} \right) = (2, 1) \] Thus, the coordinates of the mid-point \( M \) of the line segment \( AB \) are \( (2, 1) \).
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