Question

A line passes through `(9 ,8 )` and `( 3, 5 )`. A second line passes through `( 4, 8 )`. 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 `(-4,4)`.

Explanation:

A line that passes through `(9,8)` and `(3,5)` has a slope of

`(5-8)/(3-9)=(-3)/(-6)=1/2`

Hence line parallel to it must also have a slope of `1/2` and as it passes through `(4,8)`, its equation using point slope form is

#(y-8)=1/2(x-4)@

or `2y-16=x-4` or `x-2y+12=0`

Any point on `x-2y+12=0` when joined to point `(4,8)` will give a line parallel to the above.

Say `x=-4` then `-4-2y+12=0` or `y=4`

Hence, one such point is `(-4,4)`.