Find an equation for the perpendicular bisector of the line segment whose endpoints are ( 1 , − 9 ) (1,−9) and ( − 9 , − 5 ) (−9,−5).

Answer 1

Perpendicular bisector is set of points in plane equidistant from endpoints. So, if (x,y) is it's arbitrary point,then

(x - 1)² + (y + 9)² = (x + 9)² + (y + 5)²; - 2x + 1 + 18y + 81 = 18x + 81 + 10y + 25; 8y = 20x + 24; y = 5/2x + 3

Answer 2

midpoint= (-4,-7) of (1-9) and (-9,-5)

slope = (-9+5)/(1+9) = -4/10 = -2/5, negative inverse = 5/2

perpendicular bisector is

y+7 = (5/2)(x+4) in point slope form

2y+14= 5x+20

5x-2y =-6 in standard form

5x-2y +6 = 0 in general form

y = (5/2)x + 3 in slope intercept form