A line segment is bisected by a line with the equation # -7 y + 3 x = 1 #. If one end of the line segment is at #( 2 , 4 )#, where is the other end?

1 Answer
May 20, 2018

#" "#
Please read the explanation.

Explanation:

#" "#
Given :

(a) A line segment is bisected by a line.

(b) Equation of the line : # 3x-7y=1#

Find :

If one end of the line segment is at #(2,4)#, find the other.

#color(green)("Step 1 :"#

Plot the point #A(2,4)# on a coordinate plane.

Graph the line #3x-7y=1# on the coordinate plane.

Construct a perpendicular line through the point #A(2,4)# to the line with the equation #3x-7y=1#.

This is the shortest distance between the line and the point #A(2,4).#

enter image source here

#color(green)("Step 2 :"#

Mark the point of intersection of the perpendicular line and the line with the equation #3x-7y=1#.

This is the Mid-Point(O) of the required line segment we must find, in order to locate the coordinates of the other end of the line segment.

Measure the magnitude of #bar(AO)#.

#bar(AO)=3.02# units.

Using the Mid-Point (O) as the center, construct a circle with radius being the magnitude of the part of the line segment #AO#.

Radius #=3.02# units.

enter image source here

#color(green)("Step 3 :"#

Extrend the line segment #AO# with a line.

Mark the intersection of the circle and this part of the extended line.

This is our Point #B#.

Join #OB# and measure the magnitude of #bar(OB)#

#bar(OB)=3.02 # units.

Find the coordinates of the point #B#.

#B=(4.38, -1.55)#. This is our required answer.

enter image source here

Hope you find this solution process useful to your requirement.