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.
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