Question
If T was the midpoint of line segment AB, what would need to be true?
Answers
Answered by
GPT-4o mini
If \( T \) is the midpoint of line segment \( AB \), then the following must be true:
1. \( AT = TB \): The lengths of the segments \( AT \) and \( TB \) must be equal. This means that point \( T \) divides the segment \( AB \) into two equal parts.
2. The coordinates of \( T \) can be calculated as the average of the coordinates of points \( A \) and \( B \). If \( A \) has coordinates \( (x_1, y_1) \) and \( B \) has coordinates \( (x_2, y_2) \), then the coordinates of \( T \) are given by:
\[
T = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
3. \( T \) lies on the line segment between \( A \) and \( B \): Point \( T \) must be between points \( A \) and \( B \) along the path connecting them.
In summary, for \( T \) to be the midpoint of \( AB \), it must equally divide the segment \( AB \) and lie precisely in the center of that segment.
1. \( AT = TB \): The lengths of the segments \( AT \) and \( TB \) must be equal. This means that point \( T \) divides the segment \( AB \) into two equal parts.
2. The coordinates of \( T \) can be calculated as the average of the coordinates of points \( A \) and \( B \). If \( A \) has coordinates \( (x_1, y_1) \) and \( B \) has coordinates \( (x_2, y_2) \), then the coordinates of \( T \) are given by:
\[
T = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
3. \( T \) lies on the line segment between \( A \) and \( B \): Point \( T \) must be between points \( A \) and \( B \) along the path connecting them.
In summary, for \( T \) to be the midpoint of \( AB \), it must equally divide the segment \( AB \) and lie precisely in the center of that segment.