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Write the equation for the perpendicular bisector of the line segment connecting the points $(3,2)$ and $(-1,7)$ in the form $y = mx + b$.

Note: The perpendicular bisector of the line segment $\overline{AB}$ is the line that passes through the midpoint of $\overline{AB}$ and is perpendicular to $\overline{AB}$.

 Oct 25, 2023
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first find midpoint of line

 

(((x1+x2)/2),((y1+y2)/2))

= (((3-1)/2),((2+7)/2))

= (1,9/2)

 

equation of original line

1. find slope (7-2)/(-1-3) = -5/4

2. write in point slope form: y - 2= -5/4(x - 3)

3. expand into slope intercept form: y = -5/4x + 23/4

 

find slope of perpendicular line, which is -1/m, where m is original slope

-1/(-5/4) = 4/5

equation of perpendicular line passing through (1,9/2): y = 4/5x + 23/4

 Oct 25, 2023

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