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The distance from 3 to 13 is 10.  4/5 of that is 10(4/5)= 8 so 4/5 of the way from 3 to 13 is 3+ 8= 11.  The (signed) distance from -5 to -15 is -10.  4/5 of that is -10(4/5) is -8 so 4/5 of the way from -5 to -15 is -5+ (-15- (-5))(4/5)= -4+ (-10)(4/5)= -4- 8= -12.  The point 4/5 of the way  between (3, -5) to (13, -15) is (11, -12).

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4 hours ago, Rachel Maddiee said:

it should be (11,-13).

 

Gosh Rachel, you are correct.

Countryboy must have been at the moonshine again, he is normally pretty accurate and I did not check the working.

On 12/13/2019 at 10:08 PM, Country Boy said:

-5+ (-15- (-5))(4/5)= -4+ (-10)(4/5)= -4- 8= -12

Oops !

 

Did you draw the diagram?

And did you understand why the differences in x coordinates and y coordinates are also 4/5 of the way along?

coordinates1.thumb.jpg.f8a59579d94b3b3c0db4f30ddfa56d45.jpg

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2 minutes ago, Rachel Maddiee said:

Would (11,-13) be the final answer?

Yes it's my final 'answer' to the numbers.

But both your instructor and I am keen that you understood how to get there.

Which is why I suggested, and posted, a diagram.

 

and also asked you the two questions at the end.

 

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Is this correct?

 

Find the midpoint of AB first using the midpoint formula.
Midpoint = (x1 + x2/2, y1 + y2/2) 
A(3, -5)
B(13, -15)
Average x-value = (3 + 13)/2 = 8
Average y-value = (-5 + -15)/2 = -10
Midpoint is (8, -10)
Let P = point which is 4/5 of the way from A to B 
P = (3 + 4/5 x 10, -5 + 4/5 x -10)
= (3 + 8, - 5 - 😎
= (11, -13)

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2 minutes ago, Rachel Maddiee said:

In the diagram what formula did you use?

 

33 minutes ago, studiot said:

And did you understand why the differences in x coordinates and y coordinates are also 4/5 of the way along?

If you want an formula

try

 

% Change in x distance  = % change in y distance = % change in direct distance along AB all measured from A

So in this question the point is 4/5 or 80% of the distance along AB.

So is the distance from the y axis of the x coordinate and the distance from the x axis of the y coordinate.

I am abut to watch a TV programme but will look in agian in about 1 hour.

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2 hours ago, Rachel Maddiee said:

 No, I want to stick with your method. In terms of geometric explanations and justification I want to make sure I understand what you’ve used exactly.

I don't know in what order you have been learning geometry but you should have seen the properties of similar triangles before detailed plotting graphs or the coordinate geometry here.

If not I have started there since I originally said to do it by similar triangles.

This is the justification for the statement that the differences in x and y coordinates of the points is in the same ratio as the difference of the coordinates on the direct line between them.

simtri1.thumb.jpg.0ad7b9a4c376b06c9d81e3e47805f75b.jpg

 

simtri2.thumb.jpg.0679a505fa4319fe40f04fac0dd5b7d6.jpg

 

simtri3.thumb.jpg.556314d0f9e76a96651343f4f29d49be.jpg

 

 

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1 hour ago, Rachel Maddiee said:

How do I give an explanation without using graphs?

Isn't that like asking "How do I plot the points A(3, -5)  and B(13, -5) and the line segment between them without a graph?

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Maybe I'm overthinking this, but the distance between two cartesian points is given by root[(delta x)^2+(delta y)^2], which is of course, good old Pythagoras.
It occurs to me that 4/5 of that could be 80% of the distance measured  from A to B, or 80% of the distance measured from B to A.
IOW, two different points.

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27 minutes ago, MigL said:

Maybe I'm overthinking this, but the distance between two cartesian points is given by root[(delta x)^2+(delta y)^2], which is of course, good old Pythagoras.
It occurs to me that 4/5 of that could be 80% of the distance measured  from A to B, or 80% of the distance measured from B to A.
IOW, two different points.

Too much tequilla?

The OP says "from A to B"

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I have already indicated countryboy's error. His basic method is correct

Quote

The distance from 3 to 13 is 10.  4/5 of that is 10(4/5)= 8 so 4/5 of the way from 3 to 13 is 3+ 8= 11.  The (signed) distance from -5 to -15 is -10.  4/5 of that is -10(4/5) is -8 so 4/5 of the way from -5 to -15 is -5+ (-15- (-5))(4/5)= -4  -5+ (-10)(4/5)= -4  -5- 8= -12.  The point 4/5 of the way  between (3, -5) to (13, -15) is (11, -13).

So you should cross out the -4 in the two places he has used it and substitute the correct value of -5

as in the quote above

That will give you the correct coordinates as above.

I hope you understand his basic method.

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The distance from 3 to 13 is 10.  4/5 of that is 10(4/5)= 8 so 4/5 of the way from 3 to 13 is 3+ 8= 11.  The (signed) distance from -5 to -15 is -10.  4/5 of that is -10(4/5) is -8 so 4/5 of the way from -5 to -15 is -5+ (-15- (-5))(4/5)= -5 -5+ (-10)(4/5)= -5 -5- 8= -13.  The point 4/5 of the way  between (3, -5) to (13, -15) is (11, -13).

Like this?

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12 minutes ago, Rachel Maddiee said:

-5+ (-15- (-5))(4/5)= -5 -5+ (-10)(4/5)= -5 -5- 8= -13

Not quite.

Your did it correctly here, replacing -4 with -5

13 minutes ago, Rachel Maddiee said:

-5+ (-15- (-5))(4/5)=

But you did it twice for some reason here

14 minutes ago, Rachel Maddiee said:

-5 -5+ (-10)(4/5)= -5 -5- 8

So gained an extra -5.
This does not = -13!

this should of course be

=  -5+ (-10)(4/5)= -5- 8= -13.

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The distance from 3 to 13 is 10.  4/5 of that is 10(4/5)= 8 so 4/5 of the way from 3 to 13 is 3+ 8= 11.  The (signed) distance from -5 to -15 is -10.  4/5 of that is -10(4/5) is -8 so 4/5 of the way from -5 to -15 is -5+ (-15- (-5))(4/5)= -5+ (-10)(4/5)= -5- 8= -13.  The point 4/5 of the way  between (3, -5) to (13, -15) is (11, -13).

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