Find the equation of the line perpendicular to the line4x+8y=16 and through the midpoint of AB where A(-8,12) and B(6,10) Please go step by step.

Question

Find the equation of the line perpendicular to the line4x+8y=16 and through the midpoint of AB where A(-8,12) and B(6,10)  Please go step by step.

anonymous · Answer

can you fist find the midpoint of AB ?

anonymous · Answer

*first

anonymous · Answer

do u know the midpoint formula?

laddiusmaximus · Answer

using the midpoint formula, yes
(-1, 11)

anonymous · Answer

ok... good... now that we have a point, we need the slope of the line we need...

anonymous · Answer

it needs to be PERPENDICULAR to the line 4x + 8y = 16.

can you find the slope of this line?

laddiusmaximus · Answer

should be -1/2

anonymous · Answer

yes.... that's the slope of 4x + 8y = 16.....

now the line needs to be perpendicular to a slope of -1/2..
what slope would that be?

laddiusmaximus · Answer

2/1 or just 2

anonymous · Answer

corrrect... :)

anonymous · Answer

so we have a point, (-1, 11)
and the slope, m=2 

we can put that info in point-slope form:  $\large y-y_1=m(x-x_1) $

anonymous · Answer

what form does the line need to be in?

anonymous · Answer

standard form?  (like the given line in the original post?)

laddiusmaximus · Answer

it is in a different form i think the last answer was x-2y=10 which im not sure what form that is

anonymous · Answer

ok.... stick the info into point-slope form to find the equation of the line we need.
after finding that, we can put that in standard form....

laddiusmaximus · Answer

ok then its y-11=2(x+1)

anonymous · Answer

yes....

carry out distributive property on the right side to get:

y - 11 = 2x + 2

to get it in standard form bring everything with a variable to the left side and move all constants to the right...

anonymous · Answer

ie, move the 2x to the left and move the -11 to the right.

laddiusmaximus · Answer

2x+y=13

laddiusmaximus · Answer

right?

laddiusmaximus · Answer

the answer is x+2y=21 have no clue how the book got that

hero · Answer

I'll have to check over the steps

hero · Answer

4x+8y=16
4(x + 2y) = 4(4)
x + 2y = 4
2y = 4 - x
  y = (4 - x)/2
  y = 2 - x/2

The slope of the original line is definitely -1/2 so the slope of the perpendicular line should be 2.

hero · Answer

Looks like your book is wrong.

laddiusmaximus · Answer

wow. and I paid for that book too....figures

laddiusmaximus · Answer

does it always have to be in standard form? can you run that past me again?

hero · Answer

No, there are other forms. Slope Intercept is another form.