Answer :
Answer:
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Given that the two students are equidistant from a box located at the origin \((0, 0)\), we need to determine the possible position(s) of student B, given that student A is at position \((0, 7)\) and the ordinate (y-coordinate) of student B is zero.
Let's denote the position of student B as \((x, 0)\).
The distance between student A and the origin is:
\[
\sqrt{(0 - 0)^2 + (7 - 0)^2} = \sqrt{0 + 49} = 7
\]
Since student B is also equidistant from the origin, the distance between student B and the origin should also be 7. Thus, we have:
\[
\sqrt{(x - 0)^2 + (0 - 0)^2} = 7
\]
This simplifies to:
\[
\sqrt{x^2} = 7 \implies x^2 = 49 \implies x = \pm 7
\]
Therefore, the possible positions for student B are:
\[
(7, 0) \quad \text{and} \quad (-7, 0)
\]
So, the positions of student B can be:
\[
(7, 0) \quad \text{or} \quad (-7, 0)
\]