Question
\( A \) 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
Real Tutor Solution
Tutor-Verified Answer
Answer
The midpoint of \( AB \) is \( (2,\ 1) \).
Solution
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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Simplify this solution 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 \( (2, 1) \).
