Geometry: Practice Question Sets - Easy

[mac784]

Hi Everyone,

I was wondering if someone could explain the difference between no. 3 and no. 17 in the Geometry Practice Question Sets, Level Easy. In no. 3, as it is a QC, I would expect to manipulate the shape into an alternative form that satisfies the conditions but would produce alternative outcomes - basically going by the rule of: don't trust the diagram - move things around.

But by this logic, why in no. 17 then, are these lines assumed to be fixed?

In the explanation, the answer is provided with the understanding that the position of the two lines is fixed - in this case the declination of their slopes relative to one another is not 'manipulable'. Why could these lines not be 'toyed with' - to resemble a cross for example by keeping one fixed and rotating the other along the axis of the point of intersection in order to maintain what appears to be the only constraining condition, their point of intersection.

I'm confused about when to apply the "don't trust the diagram rule" and when not to?

Thanks,

[tommywallach]

Hey Mac,

Your thought process here is perfect, but there are some details that you're forgetting.

In the case of the triangle, because it isn't on a coordinate graph, you have very little knowledge (angles are undefined). That's why the answer is (D).

In this case, you know more than you think. You know:

1) Both lines have a negative slope. (Yes, the overall positive or negative slope of a line is considered a given).

2) Line m passes through the origin.

3) The x-intercept of line n is greater than the x-intercept of line m.

4) The y-intercept of line n is greater than the x-intercept of line m.

If you take these four facts, you can definitively say that the slope of line n. Do you see now how this is different from the triangle question?

-t