A line segment is bisected by a line with the equation 8 y + 5 x = 4 . If one end of the line segment is at ( 1 , 3 ), where is the other end?

1 Answer
sankarankalyanam
Oct 13, 2017

Other end coordinates (-1.809, -1.4944)

Explanation:

Assumption: It’s a perpendicular bisector that intersects the line segment.
Slope of perpendicular bisector m1;
y=-(5/8)x+(1/2)
m1=-(5/8)

Slope of line segment m2=-(1/m1)=-(1/-(5/8))=8/5
Equation of line segment :
y-3=(8/5)(x-1)
5y-15=8x-8
5y-8x=7color(white)(aaaaa)Eqn (1)
8y+5x=4color(white)(aaaaa)Eqn (2)

Solving Eqns (1) & (2) to get the midpoint coordinates,
25y-40x=35
64y+40x=32 color(white)(aaa) Adding both,
89y=67 or y=67/89=0.7528
x=(4-(8*(67/89)))/5=-0.4045
Midpoint coordinates (-0.4045,0.7528)

—0.4045=(x1+1)/2, 0.7528=(y1+3)/2
x1=-1.809, color(white)(aaaaa)y1=-1.4944

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