# 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?

##### 2 Answers

The other point is on the line

(any point on this line will satisfy the given requirement)

#### Explanation:

Given

and a point

Consider the vertical line through

This vertical line will intersect

where

The distance from

is

So a point

Note that any point on a line parallel to

If

#color(red)("L1")# parallel to#color(green)("L2")#

then#triangle ABC ~=triangle ADE#

#rarr abs(AB):abs(AD)=abs(AC):abs(AE)#

Since

Our required line will also have a slope of

and since it passes through

using the slope-point form, we have

or

The other end-pt. lies on the line given by the eqn.

#### Explanation:

Suppose that the other end-pt. is

Let the given end-pt. be

If

Now,

Therefore, co-ords. of

Hence,

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