Rachel Maddiee Posted December 13, 2019 Share Posted December 13, 2019 I need help with understanding this question. Link to comment Share on other sites More sharing options...
Country Boy Posted December 13, 2019 Share Posted December 13, 2019 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). Link to comment Share on other sites More sharing options...
Rachel Maddiee Posted December 13, 2019 Author Share Posted December 13, 2019 what formula did you use for this? Link to comment Share on other sites More sharing options...
studiot Posted December 13, 2019 Share Posted December 13, 2019 5 minutes ago, Rachel Maddiee said: what formula did you use for this? similar triangles. Hint draw a diagram showing what countryboy did. Link to comment Share on other sites More sharing options...
Rachel Maddiee Posted December 15, 2019 Author Share Posted December 15, 2019 it should be (11,-13). Link to comment Share on other sites More sharing options...
studiot Posted December 15, 2019 Share Posted December 15, 2019 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? 1 Link to comment Share on other sites More sharing options...
Rachel Maddiee Posted December 15, 2019 Author Share Posted December 15, 2019 Would (11,-13) be the final answer? Link to comment Share on other sites More sharing options...
studiot Posted December 15, 2019 Share Posted December 15, 2019 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. Link to comment Share on other sites More sharing options...
Rachel Maddiee Posted December 15, 2019 Author Share Posted December 15, 2019 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) Link to comment Share on other sites More sharing options...
studiot Posted December 15, 2019 Share Posted December 15, 2019 10 minutes ago, Rachel Maddiee said: Average x-value = (3 + 13)/2 = 8 Average y-value = (-5 + -15)/2 = -10 Midpoint is (8, -10) How does this help this problem? Link to comment Share on other sites More sharing options...
Rachel Maddiee Posted December 15, 2019 Author Share Posted December 15, 2019 In the diagram what formula did you use? Link to comment Share on other sites More sharing options...
studiot Posted December 15, 2019 Share Posted December 15, 2019 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. Link to comment Share on other sites More sharing options...
Sensei Posted December 15, 2019 Share Posted December 15, 2019 Listen to studiot. Starting from drawing diagram is the key. Link to comment Share on other sites More sharing options...
Rachel Maddiee Posted December 15, 2019 Author Share Posted December 15, 2019 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. Link to comment Share on other sites More sharing options...
studiot Posted December 16, 2019 Share Posted December 16, 2019 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. 1 Link to comment Share on other sites More sharing options...
Rachel Maddiee Posted December 16, 2019 Author Share Posted December 16, 2019 How do I give an explanation without using graphs? Link to comment Share on other sites More sharing options...
studiot Posted December 16, 2019 Share Posted December 16, 2019 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? Link to comment Share on other sites More sharing options...
MigL Posted December 16, 2019 Share Posted December 16, 2019 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. Link to comment Share on other sites More sharing options...
studiot Posted December 16, 2019 Share Posted December 16, 2019 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" Link to comment Share on other sites More sharing options...
Rachel Maddiee Posted December 16, 2019 Author Share Posted December 16, 2019 I want to write it out exactly like Country Boy did. Link to comment Share on other sites More sharing options...
studiot Posted December 16, 2019 Share Posted December 16, 2019 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. 1 Link to comment Share on other sites More sharing options...
Rachel Maddiee Posted December 16, 2019 Author Share Posted December 16, 2019 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? Link to comment Share on other sites More sharing options...
studiot Posted December 16, 2019 Share Posted December 16, 2019 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. 1 Link to comment Share on other sites More sharing options...
Rachel Maddiee Posted December 16, 2019 Author Share Posted December 16, 2019 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). Link to comment Share on other sites More sharing options...
MigL Posted December 17, 2019 Share Posted December 17, 2019 6 hours ago, studiot said: Too much tequilla? The OP says "from A to B" Ooops ! No, not tequila, Studiot. Maybe early onset dementia ? Link to comment Share on other sites More sharing options...
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