Believers are to Turn their Face Toward Al-Masjid Al-Haram / the Forbidden House
And Indeed, the Nearby Al-Aqsa Mosque Faces the Dome of the Rock and Not Mecca
As the line shows, as well as a simple examination, Al-Aqsa Mosque is aligned with the Dome of the Rock because the Dome of the Rock is the correct direction of prayer.
Neither the Dome of the Rock, Nor Al-Aqsa Mosque Face Mecca
There are Clear Signs in it Such as the Standing Place of Abraham, so Take a Place of Prayer from the Standing Place of Abraham
And Indeed, there are Visible Footprints Claimed to be on the Noble Rock Within the Dome of the Rock, which is Also a Surface in which a Place of Prayer could be Taken
3:96 - 97, Qur'an
Indeed, the first House established for mankind was that at Bakkah - blessed and a guidance for the worlds. There are clear signs in it [such as] the standing place of Abraham.
2:125, Qur'an
[So] take a place of prayer from the standing place of Abraham.
However, they Falsely Claim that these Footprints Belong to Muhammad Instead of Abraham
In fact, at the south-western side of the Noble Rock, it is believed that the blessed footprint of the Prophet (saw) is still visible there. SubhanAllah! - MuslimHands.org
The exposed bedrock directly under the dome — known as the Noble Rock to Muslims — is the spot from which Islamic tradition indicates Prophet Muhammad ﷺ ascended to heaven, and according to Islamic tradition. It is believed that the Stone tried to follow Prophet Muhammad ﷺ as he ascended, leaving his footprint here while pulling up and hollowing out the cave below. - AtlasIslamica
And they Claim that Abraham's Footprints are Kept within a Structure Outside of the Kaaba, Instead of it Being a Clear Sign in the House of Abraham
The Qur'an states that there are clear signs in the House, such as the standing place of Abraham, and yet these footprints are housed in a golden structure outside of the Kaaba.
This Makes it Impossible to Take a Place of Prayer from them, Since they are Housed within a Structure
The Qur'an also says to take a place of prayer from the standing place of Abraham, which is impossible if his footprints are in this structure.
And Indeed, you Pass by the Ruins of the People of Lot in the Morning and at Night, for they are on an Established Road
And Thus, the People of Muhammad Passed by Sodom and Gomorrah in the Morning and at Night, which Suggests that these Ruins are Within a Reasonable Proximity to Bakkah
37:133 - 138, Qur'an
And indeed, Lot was among the messengers. [So remember] when We saved [Lot] and his family, all, except an old woman among those who remained [with the evildoers]. Then We destroyed the others [of Sodom and Gomorrah]. And indeed, you pass by them in the [early] morning and at night. Then will you not use reason?
15:76 - 79, Qur'an
[For] indeed, [Sodom is situated] on an established road. Indeed, there is a sign in that for the believers. And the companions of the thicket were [also] wrongdoers. So We took retribution from them, and indeed, both [cities] are on a clear highway.
The ruins of the people of Lot are along a clear path.
One of many ruined buildings from the people of Lot.
Sodom and Gomorrah are Joined at the Salt Sea, or the Dead Sea
Genesis 14:2 - 3, Torah
[These] made war with Bera, king of Sodom, and with Birsha, king of Gomorrah, Shinab, king of Admah, and Shemeber, king of Zeboiim, and the king of Bela, who is Zoar. All these were joined together in the vale of Siddim, which is the Salt Sea.
And Thus, with the Ruins of Sodom and Gomorrah Being Near the Dead Sea, they would Then be Around 50 - 75 Kilometers Away from the Dome of the Rock
And if they were traveling by camel, this 50 - 75 kilometer journey could take 1 to 2 hours one way at a reasonable speed of 40 kmh. This is reasonable for allowing them to pass by their ruins twice a day, once in the morning and once at night, potentially on their journey to the Dead Sea and back home each day.
But the Ruins of Sodom and Gomorrah are Around 1,200 Kilometers from Mecca
And if they were traveling by camel, even at their top speed of 65 kmh, this 1,200 kilometer journey would still take 18 hours straight, which would make it impossible to pass by their ruins twice a day, once in the morning and once at night.
The First House Established for Mankind was Built by Abraham in Bakkah, Also Known as Shiloh, the Place Where God Set His Name at First
And Due to God is a Pilgrimage to the House for whoever can Find a Way Thereto so that they may Sacrifice to the Lord
22:33, Qur'an
[For] their place of sacrifice is at the Ancient House [of God] -
Judges 21:12, Torah
[And] Shiloh [was] in the land of Canaan.