To find the coordinates of point \( J \) on line segment \( AB \) such that the ratio \( AJ : JB = 1 : 1 \), point \( J \) must be the midpoint of segment \( AB \).
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First, identify the coordinates of points \( A \) and \( B \). However, they are not provided in the question. We would typically denote them as \( A(x_1, y_1) \) and \( B(x_2, y_2) \).
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The midpoint \( J \) of the line segment connecting points \( A \) and \( B \) can be calculated using the midpoint formula: \[ J\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right) \]
Since you provided specific coordinate options for \( J \), I will check the provided coordinates against whatever \( A \) and \( B \) represent, keeping in mind that to maintain a ratio of \( 1:1 \), \( J \) must be at the midpoint.
- \( J(0,2) \)
- \( J(3,0) \)
- \( J(0,-3) \)
- \( J(0,3) \)
Without the coordinates of points \( A \) and \( B \), it's impossible to precisely identify which of these options correctly represents \( J \). However, if we assume \( A \) and \( B \) happen to be such that \( (0,2) \) or any other options are valid midpoints, we could assess each.
To conclude, if you have specific coordinates for point \( A \) and point \( B \), please provide them to determine which option correctly represents point \( J \) as the midpoint of \( AB \).
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