Geometry Strategy guide 5 pg 75 #9

[allenwong2288]

Hi all,

Could someone provide an explanation of this problem that's different from the book? Is there anyway I can use the length of the hypotenuse, find its midpoint and go back to figure out the x and y?

Thanks,

Allen

[StaceyKoprince]

Please follow the forum rules when posting or you are going to wait forever for a reply. :) Please post the full text of the problem. If there is a graphic (as there is on this one), just indicate that the problem includes a graphic in the book.

You can find the length of the hypotenuse, as the solution does in the book, but finding the midpoint doesn't actually help in a different way, because we're looking for the piont 75% along the way, not 50% along the way. So you'd still basically have to do something along the lines of what the book did, and figuring out the midpoint would just add a step. You could, for example, figure out the midpoint, and then figure out half of the midpoint, and add that to the midpoint to get 75% of the way along... but that's just more work.

[ajhong]

Hi there, I had similar questions to this problem -- would love if you could provide a more detailed explanation as to the best way to solve this.

"What are the coordinates for the point on line AB (see figure) that is three times as far from A as from B and that is in between points A and B?"

In the explanation, they divide AB into 3x + x, which I understand. However, I don't understand why the set 4x = 3 based on the horizontal distances between points A and B being 3 units, or 4x = 6 based on the vertical distance.

Could you please provide an explanation for this? Thanks very much in advance!!

[tim]

I’m really sorry, I don’t understand your question. You ask why they set 4x = 3 based on the horizontal distance. The reason they set 4x = 3 is BECAUSE the horizontal distance is 3 and we need to split that 3 up into the 3x and x parts. It sounds like you answered your own question. Am I missing something?

[munique2]

Please follow the forum rules when posting or you are going to wait forever for a reply. :) Please post the full text of the problem. If there is a graphic (as there is on this one), just indicate that the problem includes a graphic in the book.

You can find the length of the hypotenuse, as the solution does in the book, but finding the midpoint doesn't actually help in a different way, because we're looking for the piont 75% along the way, not 50% along the way. So you'd still basically have to do something along the lines of what the book did, and figuring out the midpoint would just add a step. You could, for example, figure out the midpoint, and then figure out half of the midpoint, and add that to the midpoint to get 75% of the way along... but that's just more work.

Once you find the midpoint, let's call it M, then simply find the midpoint between M and B. This doen't really add more work. In the end it is your personal preference but I guess a few people will find it easier and faster to calculate midpoints by taking the average of two coordinate points.

[tim]

thanks!

[saurabhbanerjeeiimk]

I’m really sorry, I don’t understand your question. You ask why they set 4x = 3 based on the horizontal distance. The reason they set 4x = 3 is BECAUSE the horizontal distance is 3 and we need to split that 3 up into the 3x and x parts. It sounds like you answered your own question. Am I missing something?

Hi,
I have exactly the same question. To my understanding, what you are trying to say is that 4x = 3. i.e 3x+x=4x = 3

However, how can the hypotenuse be equal to a total of 3? In order to get 3, we calculated the run, and the run gives the horizontal distance, and not the hypotenuse.

[tim]

as discussed above, you do NOT want to calculate the hypotenuse, as that will only create extra work. with the equation you give, we are looking for the horizontal displacement. this equation (fortunately) has nothing to do with the hypotenuse..