Question

A line passes through `(3 ,2 )` and `(1 ,3 )`. A second line passes through `(1 , 4 )`. 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 would be `(3,3)`

Explanation:

The line, `L_1`, through `(3,2)` and `(1,3)` has a slope of
`color(white)("XXX")m_(L1) = (Deltay_(L1))/(Deltax_(L1))=(3-2)/(1-3)=-1/2`

The line, `L_2`, through `(color(green)(1),color(magenta)4)` must have the same slope if it is parallel to `L_1`;
that is the ratio `(Deltay_(L2)):(Deltax_(L2))` must be `color(red)((-1)k):color(blue)(2k)`

and any point on `L_2` must have the form:
`color(white)("XXX")(color(green)1+color(blue)(2 * k),color(magenta)4+color(red)((-1) * k))`

For an example of such a point, we could set `k=1`
to get the point:
`color(white)("XXX")(3,3)`