The question is write an equation for the perpendicular bisector of the line segment joining the two points? the points are (0,0)(-8,-10) 1. First we find the midpoint between (0,0) and (-8,-10) because the perpendicular bisector must pass through its midpoint. 2. Second we find the slope of the line through (0,0) and (-8,-10) 3. Third we find the slope of the perpendicular bisector by A. taking the reciprocal of the slope of the line thru (0,0) and (-5,10) B. Multiplying this result by -1, which means "changing the sign" 4. Fourth, we find the equation of the perpendicular bisector using the point-slope form. 5. Simplify Here goes: 1. First we find the midpoint between (0,0) and (-8,-10) because the perpendicular bisector must pass through its midpoint. Midpoint = ( (x1+x2)/2, (y1+y2)/2 ) Midpoint = ( [0+(-8)]/2, [0+(-10)]/2 ) Midpoint = ( -8/2, -10/2 ) Midpoint = (-4,-5) 2. Second we find the slope of the line through (0,0) and (-8,-10) y2 - y1 m = ——————— x2 - x1 (-10) - (0) m = ———————————— (-8) - (0) m = (-10)/(-8) m = 5/4 3. Third we find the slope of the perpendicular bisector by A. taking the reciprocal of the slope of the line thru (0,0) and (-5,10) reciprocal of 5/4 is 4/5 B. Multiplying this result by -1, which means "changing the sign" changing the sign of 4/5 we have -4/5 4. Fourth, we find the equation of the perpendicular bisector using the point-slope form. y - y1 = m(x - x1) where m = -4/5 and (x1,y1) = Midpoint = (-4,-5) y - (-5) = -4/5[x - (-4) ] 5. Simplify y + 5 = -4/5(x + 4) y + 5 = -4/5x - 16/5 y = -4/5x - 16/5 - 5 y = -4/5x - 16/5 - 25/5 y = -4/5x - 41/5 If you like you can put the equation in standard form by clearing of fractions, getting x term first, y term second, equal sign third and number fourth: 5y = -4x - 41 4x + 5y = -41 Edwin AnlytcPhil@aol.com