From Modi'in outward — in any direction. A concrete geographic boundary approximately 30 km from Jerusalem. Anyone beyond this radius at the time of the Pesach slaughter qualifies as "far."
רַבִּי אֱלִיעֶזֶר
1 step outside the Azarah
מֵאַסְקֻפַּת הָעֲזָרָה וָלַחוּץ
From the Temple courtyard threshold and beyond. Anyone outside the Azarah at the time of slaughter — even if they are standing in Jerusalem itself — qualifies. The threshold of the Temple is the line.
A dot appears over the ה of רְחֹקָה in the Torah text — indicating it is not "truly far." This textual hint confirms R. Eliezer's ruling: the Torah itself signals that the exemption applies even at minimal distance from the Temple.
תענית א׳:ג׳: The Furthest Point — From Sukkos to the Euphrates
Taanis 1:3 reveals the outer extreme of the pilgrimage world — and by working backwards, shows us exactly when a Babylonian pilgrim had to leave home to arrive in Jerusalem for Pesach
The Babylonian Pilgrim's Year — Working Backwards from Taanis 1:3
Rabban Gamliel rules that rain is requested on 7 Cheshvan — fifteen days after Sukkos — to allow the last Israelite to reach the Euphrates River on his way home. If the return journey to Babylonia takes 15 days, then the outbound journey to Jerusalem for Pesach also takes 15 days. Therefore a Babylonian pilgrim had to depart for Jerusalem no later than ~1 Nissan — two weeks before the Seder — in order to arrive in time to bring the Korban Pesach.
יְצִיאָה מִבָּבֶל לִירוּשָׁלַיִם
~1 Nissan → depart Babylonia for Jerusalem · 15 days
יְרוּשָׁלַיִם — פֶּסַח וְסוּכּוֹת
Pesach + Sukkos in Jerusalem
חֲזָרָה לִנְהַר פְּרָת
Return to Euphrates · 15 days · arrives ~7 Cheshvan
"So that the last Israelite may reach the Euphrates River." Rabban Gamliel's ruling about rain prayers reveals the full scale of the pilgrimage world: the furthest Jew traveled ~900 km from Jerusalem. These pilgrims were traveling a distance R. Akiva would call a דֶּרֶךְ רְחוֹקָה thirty times over.
The mishnah in Pesachim asks a precise legal question: where does "far" begin? R. Akiva draws a line at Modi'in — 30 km. R. Eliezer draws it at the Temple threshold itself. But Taanis 1:3 pulls the lens back dramatically: the furthest Jew in the world lived on the banks of the Euphrates, 900 km away. That pilgrim traveled what R. Akiva would call a distant journey thirty times over — and still came for Pesach. The halachic definition of "far" and the lived reality of "far" existed on entirely different scales. Both are Torah.