A line segment is bisected by a line with the equation # 4 y - 3 x = 2 #. If one end of the line segment is at #( 7 , 5 )#, where is the other end?
The other point is on the line
(any point on this line will satisfy the given requirement)
and a point
Consider the vertical line through
This vertical line will intersect
The distance from
So a point
Note that any point on a line parallel to
#color(red)("L1")#parallel to #color(green)("L2")#
#triangle ABC ~=triangle ADE#
Our required line will also have a slope of
and since it passes through
using the slope-point form, we have
The other end-pt. lies on the line given by the eqn.
Suppose that the other end-pt. is
Let the given end-pt. be
Therefore, co-ords. of
This shows that :
(i) the co-ords. of other end-pt. can not be uniquely derived under the given conds.
(ii) What we can say about it (the other end-pt.) is that it lies on