SOLUTION: Find the equation of the line that is equidistant from the points (-6,4) and (0,8). Write the equation in slope-intercept form. Please help me!!!

Algebra ->  Formulas -> SOLUTION: Find the equation of the line that is equidistant from the points (-6,4) and (0,8). Write the equation in slope-intercept form. Please help me!!!      Log On


   

Question 66874This question is from textbook Advanced mathematics
: Find the equation of the line that is equidistant from the points (-6,4) and (0,8). Write the equation in slope-intercept form.
Please help me!!! This question is from textbook Advanced mathematics

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The line you want will be perpendicular to the line
through the points (-6,4) and (0,8), so you know that
if y=mx + b is the equation of the line through
(-6,4) and (0,8), then the slope of the perpendicular is
-1/m. If it's midway between the points, you need to sind that
midpoint.
First find the slope you want.
%28y+-+4%29+%2F+%28x+-+%28-6%29%29+=+%288+-+4%29+%2F+%280+-+%28-6%29%29 point-slope formula
%28y+-+4%29+%2F+%28x+%2B+6%29+=+4+%2F+6%29
6%2A%28y+-+4%29+=+4%2A%28x+%2B+6%29
3y+-+12+=+2x+%2B+12
3y+=+2x+%2B+24
y+=+%282%2F3%29x+%2B+8
check this. Does this line go through (-6,4) and (0,8)?
4+=+%282%2F3%29%2A%28-6%29+%2B+8
4+=+-4+%2B+8
4+=+4
OK
8+=+%282%2F3%29%2A0+%2B+8
8+=+8
OK
The perpendicular line will have slope -+%281%2F%282%2F3%29%29+=+-%283%2F2%29
Now find midpoint between (-6,4) and (0,8)
y%5Bmid%5D+=+%288+%2B+4%29+%2F+2
y%5Bmid%5D+=+6
x%5Bmid%5D+=+%28-6+%2B+0%29+%2F+2
x%5Bmid%5D+=+-3
midpoint is (-3,6)
%28y+-+6%29+%2F+%28x+-+%28-3%29%29+=+-%283%2F2%29
2%2A%28y+-+6%29+=+%28-3%29%2A%28x+%2B+3%29
2y+-+12+=+-3x+-+9
y+=++-%283%2F2%29x+%2B+3%2F2 answer
Does it go through (-3,6)?
6+=+-%283%2F2%29%2A%28-3%29+%2B+3%2F2
6+=+9%2F2+%2B+3%2F2
6+=+6
OK