Gprep Coordinate Geometry

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Please help me with the explanation and diagram-Thanks

[GMATGuruNY]

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.

[Brent@GMATPrepNow]

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.

Target question: Is the slope of line BC negative?


We can quickly see that statements 1 and 2 (alone) are NOT SUFFICIENT.

This brings us to...
Statements 1 and 2 combined
If we draw the line segment AB with slope -1, then we get something like this:


If we add some lines parallel to the x- and y-axes, we need to recognize that we get 45-degree angles at point B


So, if we add a 37-degree angle at point B, we get two possible scenarios:
Scenario #1

or
Scenario #2


In BOTH possible scenarios, the slope of line BC is definitely negative.
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent