Explanation regarding lines

[kiransquarepants]

It says in one of the explanations that for a line passing thru origin and equidistant from two points x1,y1 and x2,y2 the midpoint of the these two points lies on the line.
and therefore you can calculate the slope by calculating the midpoint.

However isnt it also the case that this line could be parallel to a line passing thru the two points x1,y1 and x2,y2 and therefore be equidistant from the two points, in that case the slope will be equal to the slope of the line passing thru the two points

Here is the exact question

In the xy-coordinate system, what is the slope of the line that goes through the origin and is equidistant from the two points P = (1, 11) and Q = (7, 7)?

[RonPurewal]

It says in one of the explanations that for a line passing thru origin and equidistant from two points x1,y1 and x2,y2 the midpoint of the these two points lies on the line.
and therefore you can calculate the slope by calculating the midpoint.

However isnt it also the case that this line could be parallel to a line passing thru the two points x1,y1 and x2,y2 and therefore be equidistant from the two points, in that case the slope will be equal to the slope of the line passing thru the two points

Here is the exact question

In the xy-coordinate system, what is the slope of the line that goes through the origin and is equidistant from the two points P = (1, 11) and Q = (7, 7)?

you are correct; we will fix the problem.

[dmahler]

There are a couple of points of confusion regarding this question. First, a line running parallel to the line running through two points is not equidistant from those points. For a line to be equidistant from two points (x1, y1) (x2, y2), EVERY point on the line must be equidistant from the two points. A line that is parallel to the line running through the two points will only have 1 point that is equidistant from (x1, y1) and (x2, y2).

Second, this question is flawed. The origin is not actually equidistant from (1, 11) and (7, 7), so no line including the origin will be equidistant from those points. The question has, in the short term, been removed from the CAT pool. In the longer term, it will be amended and entered back into the CAT pool.

[Ben Ku]

Thanks David for the response!

(David Mahler, who posted the response above, is another of our esteemed instructors, and also helps with our materials.)