Home > Geometry > Perpendicular Bisectors

A line segment is bisected by a line with the equation # 7 y + x = 7 #. If one end of the line segment is at #(1 ,3 )#, where is the other end?

Answer 1

Claire Akin

The other end is #=(0.4,-1.2)#

Let's rewrite the line's equation.

#7y+x=7#

#7y=-x+7#

#y=-1/7x+1#................................#(1)#

The slope is #m=-1/7#

The slope of the perpendicular line is #m'=-1/m=-1/(-1/7)=7#

The perpendicular line's equation is

#y-3=7(x-1)#

#y=7x-7+3=7x-4#.......................#(2)#

The point of intersection is obtained by solving for #x# and #y# in equations #(1)# and #(2)#

#7x-4=-1/7x+1#

#7x+1/7x=4+1=5#

#50/7x=5#

#x=5*7/50=7/10=0.7#

#y=7*0.7-4=4.9-0.4=0.9#

The point of intersection is #=(0.7,0.9)#

Let the other end of the line segment be #=(a,b)#

Then,

#((a+1)/2,(b+3)/2)=(0.7,0.9)#

#a+1=2*0.7=1.4#, #=># , #a=1.4-1=0.4#

#b+3=2*0.9=1.8#, #=>#, #b=1.8-3=-1.2#

The other end is #=(0.4,-1.2)#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Caroline Aucoin

The other end of the line segment is at the point (5, 2).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.