Question

A line passes through `(0 ,5 )` and `(8 ,3 )`. A second line passes through `(7 ,1 )`. What is one other point that the second line may pass through if it is parallel to the first line?

Answer 1

One such point is `(11,0)`

Explanation:

Let this point be `(a,b)`.

As the slope of line joining `(0,5)` and `(8,3)` is

`(3-5)/(8-0)=-2/8=-1/4`

and the slope of line joining `(7,1)` and `(a,b)` should also be the same i.e.

`(b-1)/(a-7)=-1/4`

or `4b-4=-a+7`

or `a=11-4b`

Hence any line joining a point `(11-4b,b)` with `(7,1)` will be parallel to line joining `(0,5)` and `(8,3)`

Let `b=0`, then the point is `(11,0)`

graph{(x+4y-20)(x+4y-11)=0 [-8, 12, -0.8, 9.2]}