nave wrote:
If perpendicular lines m and n intersect at (0,b) in the standard (x,y) plane, what is the value of b?
(1) The slope of the line m is -1/2
(2) The point (-1,0) is on the line n
Given: Perpendicular lines m and n intersect at (0,b) Target question: What is the value of b? Statement 1: The slope of the line m is -1/2 Since line n is PERPENDICULAR to line m, we know that line n has slope 2
However, we can raise and lower the two lines so that the value of b is different.
To see what I mean, here are two possible cases:
As you can see, with each case, we get a different
value of b.
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The point (-1,0) is on the line nSo, we know that the lines are perpendicular AND line n goes through the point (-1, 0)
However, since we don't know the SLOPES of the two lines, the value of b can change.
To see what I mean, here are two possible cases:
As you can see, with each case, we get a different
value of b. Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 1 tells us that line m has slope -1/2 and line n has slope 2
Statement 2 tells us that line n passes through (-1,0)
These two pieces of information, LOCK line n into just ONE POSSIBLE line
In fact, this also means the y-intercept (0, b) is also LOCKED in.
We get:
This also means that line m is also LOCKED in.
Since both lines are now locked in, there is only one possible value of b.
Are we going to bother to actually find the value of b?
No, that would be a waste of valuable time. We need only recognize that there is ONLY ONE possible pair of lines that satisfy the two statements, which means we COULD find the value of b
Since we COULD answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
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