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anonymous

  • 4 years ago

A(1,3) B(-3,5) find the perpendicular bisector equation

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  1. anonymous
    • 4 years ago
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    i know the slope is -2

  2. anonymous
    • 4 years ago
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    Find the midpoint also, the perpendicular line will pass through this point.

  3. anonymous
    • 4 years ago
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    the midpoint is -1,4

  4. anonymous
    • 4 years ago
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    So can you write an equation for a line that passes through (-1,4) with a slope of 1/2?

  5. anonymous
    • 4 years ago
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    so it would be y-4 = 1 x-(-1) = 2 ?

  6. anonymous
    • 4 years ago
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    if slope is -2 of the original line given two vertices,therefor the slope of the perpendicular line is 1/2

  7. anonymous
    • 4 years ago
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    the answer is 2x - y = -6 but i get a different answer

  8. ash2326
    • 4 years ago
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    We have the line connecting the points A(1,3) and B(-3,5) the point which divides the line into two halves will have coordinates D(x1,y1) \[ x1= \frac{1+(-3)}{2}\] and \[y1=\frac{3+5}{2}\] so we get \[(x1,y1= (-2, 4)\] so the perpendicular bisector will pass through this point and we need one more condition like another point or slope to find out its equation here it's easy to find the slope of perependicular bisector Let the slope of AB be m1 and of the perpendicular bisector be m2 \[m1= \frac{5-3}{-3-1}\] we get \[m1= -\frac{1}{2}\] now since AB and its perpendicular bisector are perpendicular to each other \[ m1*m2=-1\] so \[m2=2\] so we have the slope m2= 2 and the line passes through D(-2, 4) so equation will be \[ \frac{y-4}{x+2}= 2\] so we get \[y-4=2x+2\] so the equation is \[y-2x+6\]

  9. ash2326
    • 4 years ago
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    \[ y-2x=6\]

  10. ash2326
    • 4 years ago
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    or it can be written as \[2x-y=-6\]

  11. anonymous
    • 4 years ago
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    isnt the mid point (-1,4)?

  12. anonymous
    • 4 years ago
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    1 + (-3) = -2 then -2 / 2 = -1

  13. anonymous
    • 4 years ago
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    since the question is the perpendicular bisector equation of the line, we will be needing the midpoint and the perpendicular slope. .

  14. ash2326
    • 4 years ago
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    sorry I made a mistake then you'll get \[ \frac{y-4}{x+1}=2\] or \[y-4=2x+2\] or \[y-2x=6\] i made mistake 2 times and fortunately got the correct answer:)

  15. anonymous
    • 4 years ago
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    nikkyster if you got the slope to =2, you calculated the slope wrong

  16. anonymous
    • 4 years ago
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    The slope of the original line is -1/2

  17. anonymous
    • 4 years ago
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    i got the slope to be -2

  18. ash2326
    • 4 years ago
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    yeah slope of line is \[-\frac{1}{2}\]

  19. anonymous
    • 4 years ago
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    I should've double checked it earlier ;p

  20. anonymous
    • 4 years ago
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    But you have the right midpoint

  21. anonymous
    • 4 years ago
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    yeah your right ! i got the slope wrong

  22. anonymous
    • 4 years ago
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    what about for midpoint with a decimal?

  23. anonymous
    • 4 years ago
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    |dw:1328422479768:dw||dw:1328422542891:dw||dw:1328422687105:dw| therefor the perpendicular slope is 2, the equation of the perpendicular line is

  24. anonymous
    • 4 years ago
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    |dw:1328422920367:dw|

  25. anonymous
    • 4 years ago
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    A(3,1) B(-3,6)

  26. anonymous
    • 4 years ago
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    the midpoint is (0,3.5) and the slope would be -5/6

  27. anonymous
    • 4 years ago
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    is this another problem?

  28. anonymous
    • 4 years ago
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    yes

  29. anonymous
    • 4 years ago
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    what's the question? prependicular equation?

  30. anonymous
    • 4 years ago
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    perpendicular ?

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