Translation:The cat and the dog are running onto the street.
I have the same question. How would you say they run "to the street" rather than "onto the street"? Do you use zu instead of auf? If so is zu followed by the dative?
Why is the provided answer given in a present progressive form, if present progressive isnt a tense in German?
Your translation is grammatical, but describes something different.
Sie laufen auf die Straße. They are running onto the street, like they were on a yawn before and now move onto the street.
Sie laufen auf der Straße. They are running on the street, like they are running from location1 to location2 and they use the street instead of the sidewalk.
Well, not exactly, rather: accusative is used as the target of a transition, while dative is used to identify the location where something is taking place, regardless of movement or change of state. That is to mean that both whether you are sitting in the garden or whether you are jumping into the pool in the garden, the garden is dative because the activity (stationary or dynamic that it may be) is taking place entirely within the garden and not implying movement away from or towards the garden from somewhere else.
Well, I can translate the examples I gave: ‘ich sitze im Garten’ (dat., answers ‘wo sitze ich?’ = ‘where am I sitting?’); ‘ich springe in den Pool’ (acc., answers ‘wohin springe ich?’ = ‘where do I jump to?’); ‘ich springe im Garten’ (dat., answers ‘wo springe ich?’ = ‘where am I while I'm jumping?’).
A different sentence using both accusative and dative with a motion verb could be: ‘Hans geht ins Bett [accusative, direction] in seinem Haus [dative, location]’ = ‘Hans goes to bed in his own house’.
I might say into, but onto sounds so off for this example (for the English translation). (I would say ran into the street, fell on(to) the pavement. Ran onto the ice maybe, but not the street.)
The correct English expression would be "into the street" not onto. You could run onto a path or a road as it is more specific. The street is a general area hence "into". Details...
I don't understand why on the street is incorrect. Why does it have to be onto the street?
Because the accusative (‘die Straße’) is used, indicating that the cat and the dog are not running up and down the street, but they are instead going from a place that isn't the street onto the street. ‘Running on the street’ would be ‘auf der Straße laufen’.