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.
The OA is C.
Why can't the line AB be at a different degree? The slope is given as -1. Is it not possible to have the line/slope(-1) AB at any other degree other than 45?
Thanks.
In the xy-plane, points A, B and C are not on the same line
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Target question: Is the slope of line BC negative?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.
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:
![Image](https://s18.postimg.cc/7it4g711x/slope_1a.jpg)
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
![Image](https://s18.postimg.cc/99c5hoil1/slope_1b.jpg)
So, if we add a 37-degree angle at point B, we get two possible scenarios:
Scenario #1
![Image](https://s18.postimg.cc/3npqdmhw5/slope_1c.jpg)
or
Scenario #2
![Image](https://s18.postimg.cc/rsqfvc26t/slope_1d.jpg)
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