In the xy-plane, points A, B and C are not on the same line. Is the slope of line BC negative?
1. The slope of line AB is -1.
2. The measure of angle ABC is 37 degrees.
Neither statement alone is sufficient to determine the slope of BC.
Statements combined:
To see the reasoning more easily, let point B be at the origin:
In the figure above, AB has a slope of -1 and passes through the origin.
The figure shows the following:
If ∠ABC = 45º, then BC is either the x-axis (with a slope of 0) or the y-axis (with a undefined slope).
If ∠ABC > 45º, then BC will have a POSITIVE SLOPE, as illustrated by the dashed line in blue.
Since statement 2 requires that ∠ABC < 45º, the slope of BC cannot be 0, undefined, or positive.
Thus, the slope of BC must be NEGATIVE.
SUFFICIENT.
The correct answer is
C.
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