anonymous
  • anonymous
solve
Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
The line x -5y +10=0 bisects the join of (c,5) and (3,-4) find the value of c
Jim766
  • Jim766
I believe this is asking at what point does this line cross the absolute middle of the segment (c,5) and (3,-4) do you know how to find the mid point of a line segment?
anonymous
  • anonymous
yes

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Jim766
  • Jim766
in this case we can only find the y part of the mid point add the two y's together and divide by 2 5 + -4 = 1, then divide by 2 = 1/2 so the y of the mid point would be .5 make sense?
Jim766
  • Jim766
here is our strategy for finding c. we are going to use the line a the partial points of the line segment to find the midpoint once we have the mid point, of the line segment we can find the end point and c. so if the y part of the mid point is .5, we can sub it in to x -5y +10=0 to find the x x - 5(.5) + 10 = 0 x - 2.5 + 10 = 0 x + 7.5 = 0 x = -7.5 so the mid point of the line segment is (.5, -7.5) we know this, because the line can only cross the line segment at one point, and they tell us, that it is the bisector.
Jim766
  • Jim766
so do you know how to find an end point when you have a midpt and 1 endpt?
anonymous
  • anonymous
so, what to do next
Jim766
  • Jim766
sorry I wrote the mid wrong above, I reversed it it should be (-7.5, .5) mult the mid point by 2 and subtract the end we know 2* (-7.5, .5 ) = ( -15, 1) - (3, -4) -------- ( 12, 5) is the end point c = 12
Jim766
  • Jim766
make sense?
anonymous
  • anonymous
how ur end point came, -15,1 and 3, -4
Jim766
  • Jim766
to find mid point, you add the ends and divide by 2 when you have a mid and a end you take the mid *2 and then subtract the end you know
anonymous
  • anonymous
i didn't understand this step mult the mid point by 2 and subtract the end we know 2* (-7.5, .5 ) = ( -15, 1) - (3, -4) -------- ( 12, 5) is the end point c = 12
Jim766
  • Jim766
sorry, you are right there is an error,,,duh -15 - 3 = -18 the point should be (-18, 5) c = -18 my bad (-18, 5) + (3, -4) -------- -15, 1 (-15/2, 1/2) = mid (-7.5, .5)
Jim766
  • Jim766
apologies
anonymous
  • anonymous
i m not understanding how your -15 - 3 = -18 came plse help me to understand ths
Jim766
  • Jim766
you don't understand that -15 -3 is the same as -15 + (-3) = -18 or is it something else?
anonymous
  • anonymous
mid point of (c,5) & (3,-4) is \[\left( \frac{ c+3 }{ 2 },\frac{ 1 }{ 2 } \right)\] Because it lies on line x-5y+10=0 \[\frac{ c+3 }{ 2 }-5*\frac{ 1 }{ 2 }+10=0\] or c+3-5+20=0 c+18=0 c=-18

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