In a rectangular coordinate system, does point (0, 0) lie on line m ?

C imo .
In a rectangular coordinate system, does point (0, 0) lie on line m ?

(1) Line m does not pass through point (2, 0).
-- Line can pass through any point .. Not sufficient .
(2) Line m passes through point (1, 0).
-- Line can pass through any point .. Not sufficient .

Combining 1 and 2 .. If a line can pass through (1,0) and (2,0) then we can definitely tell that line will pass through point (0,0) .
So Sufficient .

Ans C

Solution

Step 1: Analyse Question Stem

• m is a straight line
• We need to find out if line m passes through origin i.e. (0,0) or not.

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE

Statement 1: Line m does not pass through point (2, 0).

• This statement only says that line m does not pass through point (2,0)

o So, line m may pass through (0,0) or it may pass through any other point on the x axis.

Hence, statement 1 is NOT sufficient and we can eliminate answer Options A and D.

Statement 2: Line m passes through point (1, 0).

• According to this statement, there can be two cases:

o Case 1: line intersect the x axis at only one point.

 In that case, the line m will pass through (1, 0) but it won’t pass through (0,0)
o Case 2: line coincides with x-axis or the line is y = 0

 In that case, the line m will pass through (1, 0) and it will pass through (0,0) as well.
• We are getting contradictory results.

Hence, statement 2 is also NOT sufficient and we can eliminate answer Option B.

Step 3: Analyse Statements by combining.

• From statement 1:

o Line m does not pass through point (2, 0).
• From statement 2:

o Case 1: line intersect the x axis at only one point i.e. (1,0).
o Case 2: line coincides with x axis or the line is y = 0.
• On combining both, we get,

o line intersect the x axis at only one point i.e. (1,0).

Thus, the correct answer is Option C.

In a rectangular coordinate system, does point (0, 0) lie on line m ?

(1) Line m does not pass through point (2, 0).
(2) Line m passes through point (1, 0).

Answer is C

Since is the line passes through (1,0) but not (2,0), the slope of the line cannot be 0.
If the slope of the line is not 0, and it passes through (1,0) then it cannot pass through (0,0)

Hence C

On combining both we can say that line doesn't pass through (0,0) . So, C

In a rectangular coordinate system, does point (0, 0) lie on line m ?

(1) Line m does not pass through point (2, 0).
(2) Line m passes through point (1, 0).

1) Depending on the slope of the line, it can either pass the origin of the coordinate plan or not. From knowing that lime m does not pass through point (2,0), we cannot find whether it passes through (0,0). not sufficient.

2) The line cannot pass through the origin, as in that case it will be the x- axis itself. Sufficient.

B is the answer.

Hi,

I see a lot of people answering this question with intuition and without mathematical rigour.

I think a complete solution to this question should look like this:

(1) We can find contradicting examples. The graph f(x)=2 doesn't pass through (2,0) by definition, and also not through (0,0). However, f(x)=3x passes through (0,0) and not through (2,0) and (0,0). We have found an example for and against the argument, so not sufficient
(2) We can find contradicting examples. f(x)=x-1 passes through (1,0), but for x=0, we get (0,-1). But for f(x)=0 we get a line with (0,0) and (1,0), and we have a contradiction again.

(1) and (2): Every line is defined uniquely by two distinct points. For a line to pass through (1,0) and the origin, it has also to pass through (2,0), since the unique line is then defined by f(x)=0. Therefore, the line can't pass through (0,0).

Hi all, I am a bit confused by the reasoning here. Appreciate if anyone can comment on the reasoning below.

(1) and (2) combined says that line m is not an x-axis but what if the line is y-axis?

In that case, the line will not pass through (2,0) and (1,0) but will pass through the origin.

In case the line isn't y-axis, it will not pass through the origin.

Hence, I feel the answer should be E.