MGMAT Advanced Quant, Ch 7, In-Action Question 2

[budoshi]

Q2: Line K&L intersect in the coordinate plane at point (3,02). Is the largest angle formed at the intersection between these two lines greater than 90degrees?
1) Lines K&L have positive y-axis intercepts
2) The distance between the y-axis intercepts of lines K&L is 5.

Answer is D...I dont understand the explantion for why 2) is SUFFICIENT. The visual solution provided in the book is not really clear/coherent (at least to me). Is there a more straightforward explantion for this?

[RonPurewal]

Q2: Line K&L intersect in the coordinate plane at point (3,02). Is the largest angle formed at the intersection between these two lines greater than 90degrees?
1) Lines K&L have positive y-axis intercepts
2) The distance between the y-axis intercepts of lines K&L is 5.

Answer is D...I dont understand the explantion for why 2) is SUFFICIENT. The visual solution provided in the book is not really clear/coherent (at least to me). Is there a more straightforward explantion for this?

hi, please post...

* ... a brief summary of what's in the diagram (moderators don't always, or even usually, have the books readily available while posting on forums)
thanks for posting the problem; please do the same with the solution (or a description of it).

* ... what, specifically, you found hard to understand about the diagram.
if you don't give us specifics, we will probably just wind up giving you an explanation that's equivalent to what is already there.

finally, you wrote the coordinates of the point as "(3,02)". is that supposed to be (3, 2)?

thanks!

[budoshi]

thanks for the response....I actually get the visual solution after having typed it out step by step.

The solution says that we need to generate a line that is perpendicular, since it is easy to generate a line that is not perpendicular....
It goes on to say that to spread the lines as far apart as possible (which I understand given that the angle that k & l must for need to be perpendicular for the largest possible distance), the "distance of 5" should be placed directly opposite the "thumbtack" (which is the point 3,-2 - my error in the original post).

By symmetry, half of that distance 5 will be above the point (3,-2)...it goes on to draw a right triangle within the larger triangle of (3,-2), y-intercept of line k and y-intercept of line l. The base is 2.5units (on the y-axis), height is the length 3 (which is drawn from the y-axis to the point 3,-2 and the hypotenuse is the lenght of point (3,-2) to the y-intercept of line k. It goes on to label the angle opposite the 2.5unit length as angle "a".

Using properties of angles, the solution then deduces that angle "a", is less than 45degrees....WHICH I ACTUALLY NOW GET having typed it out.

[tim]

let us know if there are any further questions on this one..