Distinct Line K and L intersect at (3, -2)

[muhammedz786]

Distinct Line K and L intersect at (3, -2) (in coordinate plane). Is the larger angle formed at the intersection between these two lines are greater than 90 deg?

1) Lines k and l have positive y - axis intercepts

2) The distance between the y-axis intercepts of lines k and l is 5.


I saw this problem in MGMAT advanced quant book chap 7 problem set #4. I understand the first half of the answer explanation. However, I cannot understand the second part.

Can someone please help. I added the answer choices below.

[GMATGuruNY]

Lines k and l intersect in the coordinate plane at point (3, -2 ). Is the largest angle formed at the intersection between these two lines greater than 90°?

(1) Lines k and l have positive y-axis intercepts.
(2) The distance between the y-axis intercepts of lines k and l is 5.

If lines k and l are perpendicular, they will form four 90 degree angles.
If lines k and l are not perpendicular, they will form two angles less than 90 degrees and two angles greater than 90 degrees.

Question rephrased: Are lines k and l perpendicular?

Many slope questions are best solved by DRAWING.

Statement 1:
Since each line has a positive y-intercept and passes through (3,-2), the two lines cannot be perpendicular:

SUFFICIENT.

Statement 2:
Case 1: Lines k and l are perpendicular, and the two y-intercepts are EQUIDISTANT from (3,-2).

Here, the distance between the y-intercepts = 6.

Case 2: Lines k and l are perpendicular, and the two y-intercepts are NOT EQUIDISTANT from (3,-2).

Here, the distance between the y-intercepts > 6.

Thus, if lines k and l are perpendicular, the MINIMUM distance between the y-intercepts is 6.
Since statement 2 indicates that the distance between the y-intecepts is 5, lines k and l are not perpendicular.
SUFFICIENT.

The correct answer is D.