A motorist drives from point A (16, 28) in a straight line toward his home at point B (57, 63). He stops for gas when he is half way to his destination. How far from home is the motorist when he stops for gas? Assume the units are in miles. Round to the nearest tenth.
is the answer 30.0?

Question

A motorist drives from point A (16, 28) in a straight line toward his home at point B (57, 63). He stops for gas when he is half way to his destination. How far from home is the motorist when he stops for gas? Assume the units are in miles. Round to the nearest tenth.
is the answer 30.0?

anonymous · Answer

how did you get 30.0 as the answer?

anonymous · Answer

square root of [(57 - 13)^2 + (63 - 28)^2]

anonymous · Answer

and divide that by two

aripotta · Answer

attachment

aripotta · Answer

why'd you divide by 2?

anonymous · Answer

because he stops half way there

anonymous · Answer

Ari, it's the midpoint, not the full distance

I didn't get 30 though.

aripotta · Answer

ah, i see. i didn't read the question all the way lol my b.

anonymous · Answer

i got 30.9 the second time, i can't figure out if im doing anything weird

anonymous · Answer

square root of [(57 - 13)^2 + (63 - 28)^2]   has a typo in it.

Should have been a 16 instead of 13 in that first term.

anonymous · Answer

yes it does, i had made a mistake when typing it up

aripotta · Answer

wait, so just find the midpoint and then do the distance formula with one point and the midpiont?

anonymous · Answer

@AriPotta, your formula is for the coordinate of the midpoint, but the question requires the distance.  You could solve for distance from the midpoint to the destination... would be same result.

anonymous · Answer

so it doesn't matter how i do it?

aripotta · Answer

ugh nvm. idk why i try to help anymore

anonymous · Answer

No, both approaches should be the same...

anonymous · Answer

I get 27.0

anonymous · Answer

@AriPotta  don't quit, you weren't wrong...

anonymous · Answer

okay i will try again, thanks for the help

anonymous · Answer

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anonymous · Answer

Doesn't matter if you find the distance formula for the whole route, then divide by 2, or if you follow @AriPotta's approach, you could find the actual midpoint first, then do the distance formula from that point to either end... you just don't divide that distance by 2 since it's already the half-way distance.

anonymous · Answer

so either way works and i should get the answer right?

anonymous · Answer

hopefully :)

anonymous · Answer

thank you

anonymous · Answer

yes, I just checked... with both approaches, you should end up with 26.95, rounded to nearest tenth, making it 27.0